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Journal articles on the topic 'Generalized Legendre's associated function'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Yashwant, Singh, and Kumar Mandia Harmendra. "ON AN EXPANSION FORMULA FOR THE MULTIVARIABLE I - FUNCTION INVOLVING GENERALIZED LEGENDRE'S ASSOCIATED FUNCTION." International Journal of Research – Granthaalayah 4, no. 1 (2017): 55–62. https://doi.org/10.5281/zenodo.848169.

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The authors have established a new expansion formula for multivariable I -function due to Prasad [5] in terms of products of the multivariable I -function and the generalized Legendre’s associated function due to Meulenbeld [3]. Some special cases are given in the last.

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2

Virchenko, N. A. "Applications of Legendre's generalized associated functions." Ukrainian Mathematical Journal 39, no. 2 (1987): 124–30. http://dx.doi.org/10.1007/bf01057490.

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3

Ayant, F. Y. "On an expansion formula for the multivariable aleph-function involving generalized Legendre's associated function." International Journal of Mathematics Trends and Technology 33, no. 1 (2016): 67–73. http://dx.doi.org/10.14445/22315373/ijmtt-v33p510.

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4

Singh, Yashwant, and Harmendra Kumar Mandia. "ON AN EXPANSION FORMULA FOR THE MULTIVARIABLE -FUNCTION INVOLVING GENERALIZED LEGENDRE’S ASSOCIATED FUNCTION." International Journal of Research -GRANTHAALAYAH 4, no. 1 (2016): 55–62. http://dx.doi.org/10.29121/granthaalayah.v4.i1.2016.2843.

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The authors have established a new expansion formula for multivariable -function due to Prasad [5] in terms of products of the multivariable -function and the generalized Legendre’s associated function due to Meulenbeld [3]. Some special cases are given in the last.

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5

Ayant, Frédéric. "An expansion formula for multivariable Gimel-function involving generalized Legendre Associated function." International Journal of Mathematics Trends and Technology 56, no. 4 (2018): 223–28. http://dx.doi.org/10.14445/22315373/ijmtt-v56p532.

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6

Cohl, Howard S., and Diego E. Dominici. "Generalized Heine’s identity for complex Fourier series of binomials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (2010): 333–45. http://dx.doi.org/10.1098/rspa.2010.0222.

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In his treatise, Heine ( Heine 1881 In Theorie und Anwendungen ) gave an identity for the Fourier series of the function , with , and z >1, in terms of associated Legendre functions of the second kind . In this paper, we generalize Heine’s identity for the function , with , and , in terms of . We also compute closed-form expressions for some .

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7

Dassani*, Mamta, and Mukesh kushwaha. "Some Generalized Results to unify Classical Polynomials." International Journal of Basic Sciences and Applied Computing 3, no. 3 (2021): 1–5. http://dx.doi.org/10.35940/ijbsac.b0201.033321.

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Present work of this paper deals with the unification of classical polynomials in which we have defined a generalized polynomial set analogous to that of associated Legendre polynomial P (x) m n by taking 5the use of Operator. Also we have derived explicit form, Operational Formulae generating functions for this function.

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8

MamtaDassani and kushwaha Mukesh. "Some Generalized Results to unify Classical Polynomials." International Journal of Basic Sciences and Applied Computing (IJBSAC) 3, no. 3 (2021): 1–5. https://doi.org/10.35940/ijbsac.B0201.033321.

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Present work of this paper deals with the unification of classical polynomials in which we have defined a generalized polynomial set analogous to that of associated Legendre polynomial P (x) m n by taking 5the use of Operator. Also we have derived explicit form, OperationalFormulae generating functions for this function.

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9

Ayant, Frédéric. "A Study of Unified Fractional Integral Operator Involving Generalized Laguerre Function and (т,ᵦ)-Generalized Associated Legendre Function". International Journal of Mathematics Trends and Technology 61, № 2 (2018): 117–23. http://dx.doi.org/10.14445/22315373/ijmtt-v61p517.

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10

Roditty-Gershon, Edva, Chris Hall та Jonathan P. Keating. "Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t]". International Journal of Number Theory 16, № 05 (2019): 1013–30. http://dx.doi.org/10.1142/s1793042120500529.

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We compute the variances of sums in arithmetic progressions of generalized [Formula: see text]-divisor functions related to certain [Formula: see text]-functions in [Formula: see text], in the limit as [Formula: see text]. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when [Formula: see text], in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual [Formula: see text]-divisor function, when

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11

Chowdhury, Md, Sujit Sen, Anjan Chowdhury, and Mohammad Ahammad. "On the Motion Past a Slip-Stick Sphere and a Shear Free Sphere in a Viscous Fluid." Engineering and Applied Sciences 9, no. 2 (2024): 34–42. http://dx.doi.org/10.11648/j.eas.20240902.11.

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The theoretical development of the complex fluid flows such as more than one obstacle with different shapes have great interest for scientists to understand flow phenomena and verify the model or approximate solution. The complex physical properties due to a uniform streaming motion past two fixed spheres is investigated having one with shear stress and another being shear stress-free. This study concerns analytical technique of a steady incompressible viscous fluid past to two fixed spheres. The Gegenbaur function and associated Legendre polynomials is used to derive the solution that simplif

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12

Frédéric, Ayant, Kumar Prvindra, and Singh Harendra. "On unified infinite integral involving product of multivariable Gimel-function and others special functions." APPLIED SCIENCE PERIODICAL XXIII, no. 3, August 2021 (2021): 1–16. https://doi.org/10.5281/zenodo.6796914.

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              The multivariable Gimel function [2] is an unified special function, it’s an extension of the multivariable Aleph-function defined by Ayant [1], the multivariable I-function defined by Prasad [9], the multivariable I-function defined by Prathima et al. [11] at a time, of course this function is a generalization of the multivariable H-function. To define this function, we use the multiple Mellin-Barnes integrals contour. 

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13

Śloderbach, Z. "Closed system of coupling effects in generalized thermo-elastoplasticity." International Journal of Applied Mechanics and Engineering 21, no. 2 (2016): 461–83. http://dx.doi.org/10.1515/ijame-2016-0028.

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Abstract In this paper, the field equations of the generalized coupled thermoplasticity theory are derived using the postulates of classical thermodynamics of irreversible processses. Using the Legendre transformations two new thermodynamics potentials P and S depending upon internal thermodynamic forces Π are introduced. The most general form for all the thermodynamics potentials are assumed instead of the usually used additive form. Due to this assumption, it is possible to describe all the effects of thermomechanical couples and also the elastic-plastic coupling effects observed in such mat

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14

Koinov, Z. G. "Collective Modes of an Ultracold6Li-40K Mixture in an Optical Lattice." Advances in Condensed Matter Physics 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/952852.

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A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a

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15

Li, Zheng Jun, Kai Yang, Tan Qu, Jing Bai, and Qing Chao Shang. "Analysis on scattering and inner near-field characteristics of a uniaxial anisotropic sphere by an off-axis high-order Bessel (vortex) beam." Journal of the Optical Society of America A 41, no. 11 (2024): 2054. http://dx.doi.org/10.1364/josaa.529144.

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Based on the generalized Lorenz–Mie theory (GLMT) and the Fourier transform method, a theoretical approach is introduced to study the scattering of a uniaxial anisotropic sphere illuminated by an off-axis high-order Bessel (vortex) beam (HOBVB). According to the orthogonality of the associated Legendre function and exponential function, a concise expression of the expansion coefficients of the off-axis HOBVB in terms of the spherical vector wave functions (SVWFs) is derived that can effectively reconstruct the HOBVB with all conical angles. The differences of scattering characteristics of a un

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16

Barbaresco, Frédéric. "Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation." Entropy 22, no. 6 (2020): 642. http://dx.doi.org/10.3390/e22060642.

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In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (e.g., Galileo’s group in classical physics)

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17

Kalla, S. L., N. Virchenko, and O. Lisetska. "Some results involving generalized associated Legendre functions." Integral Transforms and Special Functions 23, no. 2 (2012): 105–14. http://dx.doi.org/10.1080/10652469.2011.564379.

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18

Cohl, Howard S., and Roberto S. Costas-Santos. "Multi-Integral Representations for Associated Legendre and Ferrers Functions." Symmetry 12, no. 10 (2020): 1598. http://dx.doi.org/10.3390/sym12101598.

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For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions generalize some classical multi-integration formulas. As a result of the determination of these formulae, we compute some interesting special values and integral representations for certain particular combinations of the degree and order, including the case where there is symmetry and antisymmetry for the degree and order parameters. As a consequence of our analysi

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19

Singh, B. M., J. Rokne, and R. S. Dhaliwal. "The Study of Triple Integral Equations with Generalized Legendre Functions." Abstract and Applied Analysis 2008 (2008): 1–12. http://dx.doi.org/10.1155/2008/395257.

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A method is developed for solutions of two sets of triple integral equations involving associated Legendre functions of imaginary arguments. The solution of each set of triple integral equations involving associated Legendre functions is reduced to a Fredholm integral equation of the second kind which can be solved numerically.

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20

Fedotova, I. A. "On an integral transform with generalized associated Legendre functions." Journal of Mathematical Sciences 68, no. 6 (1994): 759–65. http://dx.doi.org/10.1007/bf01672644.

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21

Virchenko, N. A., and I. A. Fedotova. "Some properties of generalized associated Legendre functions of second kind." Journal of Mathematical Sciences 69, no. 6 (1994): 1395–403. http://dx.doi.org/10.1007/bf01250582.

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22

Giacaglia, Giorgio E. O. "Hansen Coefficients and Generalized Spherical Harmonics." Publications of the Astronomical Society of Japan 39, no. 1 (1987): 171–78. https://doi.org/10.1093/pasj/39.1.171.

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Abstract Hansen's coefficients for the Fourier series in terms of the mean anomaly correspond to a rotation of the orbital plane proportional to the eccentricity of the orbit. Here, they are given in terms of Bessel functions and generalized associated Legendre functions. These functions arise naturally when one considers the transformation of spherical harmonics under rotation.

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23

Maier, Robert S. "Legendre functions of fractional degree: transformations and evaluations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2188 (2016): 20160097. http://dx.doi.org/10.1098/rspa.2016.0097.

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Associated Legendre functions of fractional degree appear in the solution of boundary value problems on wedges or in toroidal geometries, and elsewhere in applied mathematics. In the classical case when the degree is half an odd integer, they can be expressed using complete elliptic integrals. In this study, many transformations are derived, which reduce the case when the degree differs from an integer by one-third, one-fourth or one-sixth to the classical case. These transformations or identities facilitate the symbolic manipulation and evaluation of Legendre and Ferrers functions. They gener

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24

Sanjhira, Reshma R., and B. I. Dave. "A general matrix series inversion pair and associated polynomials." Mathematica Slovaca 72, no. 6 (2022): 1471–88. http://dx.doi.org/10.1515/ms-2022-0100.

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Abstract In the present work, a pair of general inverse matrix series relations is established, and thereby a general class of matrix polynomials is introduced. This class generalizes the extended Jacobi polynomials and their particular cases such as the polynomials of Brafman, Jacobi, Chebyshev, and Legendre. It is further shown that this pair also gives rise to the matrix forms of the Wilson polynomials and the Racah polynomials. For these polynomials, the generating matrix function relations as well as the matrix summation formulas are deduced from their respective inverse pairs. Certain in

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25

Tayyah, Adel Salim, Waggas Galib Atshan, and Georgia Irina Oros. "Third-Order Differential Subordination Results for Meromorphic Functions Associated with the Inverse of the Legendre Chi Function via the Mittag-Leffler Identity." Mathematics 13, no. 13 (2025): 2089. https://doi.org/10.3390/math13132089.

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In this paper, we derive novel results concerning third-order differential subordinations for meromorphic functions, utilizing a newly defined linear operator that involves the inverse of the Legendre chi function in conjunction with the Mittag-Leffler identity. To establish these results, we introduce several families of admissible functions tailored to this operator and formulate sufficient conditions under which the subordinations hold. Our study presents three fundamental theorems that extend and generalize known results in the literature. Each theorem is accompanied by rigorous proofs and

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26

FAKHRI, H., and B. MOJAVERI. "GENERALIZED COHERENT STATES FOR THE SPHERICAL HARMONICS $Y_{m}^{m}(\theta,\phi)$." International Journal of Modern Physics A 25, no. 10 (2010): 2165–70. http://dx.doi.org/10.1142/s0217751x10048226.

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The associated Legendre functions [Formula: see text] for a given l-m, may be taken into account as the increasing infinite sequences with respect to both indices l and m. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics [Formula: see text].

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27

Ayant, F. Y. "A study of unified results involving a product of generalized Legendre's function, a general class of polynomials, Aleph-function with the multivariable Aleph-function." International Journal of Mathematics Trends and Technology 37, no. 2 (2016): 92–101. http://dx.doi.org/10.14445/22315373/ijmtt-v37p514.

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28

Ayant, Frédéric. "A study of unified results involving a product of generalized Legendre's function, a general class of polynomials, Aleph-function with the multivariable I-function." International Journal of Mathematics Trends and Technology 39, no. 3 (2016): 181–88. http://dx.doi.org/10.14445/22315373/ijmtt-v39p522.

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29

Mináč, Ján, Lyle Muller, Tung T. Nguyen, and Nguyễn Duy Tân. "On the Paley graph of a quadratic character." Mathematica Slovaca 74, no. 3 (2024): 527–42. http://dx.doi.org/10.1515/ms-2024-0040.

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Abstract Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches of mathematics. Classically, for each prime number p we can construct the corresponding Paley graph using quadratic and non-quadratic residues modulo p. Therefore, Paley graphs are naturally associated with the Legendre symbol at p which is a quadratic Dirichlet character of conductor p. In this article, we introduce the generalized Paley graphs. These are graphs that are associated with a general quadratic

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30

Aleksandrov, Alexander G. "On Multivariate Picard–Fuchs Systems and Equations." J 6, no. 3 (2023): 437–59. http://dx.doi.org/10.3390/j6030029.

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In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting properties of such systems and relationships between them. Then we show how to calculate the fundamental solutions to the Gauss–Manin system for Aμ-singularities and to the corresponding generalized Legendre equations in terms of the multidimensional Horn’s hypergeometric functions. In conclusion, some important questions concerning basic properties of the local

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31

Chang, Seung Jun, Hyun Soo Chung, and Jae Gil Choi. "Sequential transforms associated with Gaussian processes on function space." International Journal of Mathematics 27, no. 04 (2016): 1650031. http://dx.doi.org/10.1142/s0129167x16500312.

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We define two generalized sequential transforms on the function space [Formula: see text]. In order to find the essential structure of the generalized sequential transforms we first investigate the relationships between the generalized analytic [Formula: see text]-Feynman integral and the generalized [Formula: see text]-function space integral. We then establish the existences of our sequential transforms on [Formula: see text]. One of these sequential transforms identifies the generalized analytic [Formula: see text]-Fourier–Feynman transform and the other transform plays a role as an inverse

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32

Ali, Rana Safdar, Saba Batool, Shahid Mubeen, et al. "On generalized fractional integral operator associated with generalized Bessel-Maitland function." AIMS Mathematics 7, no. 2 (2022): 3027–46. http://dx.doi.org/10.3934/math.2022167.

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<abstract><p>In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.</p></abstract>

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33

Ben Nakhi, Y., and S. L. Kalla. "A generalized beta function and associated probability density." International Journal of Mathematics and Mathematical Sciences 30, no. 8 (2002): 467–78. http://dx.doi.org/10.1155/s0161171202007512.

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We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are derived. Some special cases are mentioned. Some figures for pdf, hazard rate function, and mean residue life function are given. These figures reflect the role of shape and scale parameters.

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34

Olusegun, Hamzat J. "Subordination Results Associated With Generalized Bessel Functions." Journal of Nepal Mathematical Society 2, no. 1 (2019): 57–64. http://dx.doi.org/10.3126/jnms.v2i1.33016.

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In the present work, subordination results for function f(z)γ belonging to a new class of analytic function Snγ (α, β, j) defined using the concept of Hadamard product are obtained. Also coeffcient estimates, growth and distortion properties for function f(z)γ in the class RSnγ (α, β, j) of Bessel type are equally investigated.

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35

Choi, Junesang, Rakesh K. Parmar, and Purnima Chopra. "Extended Mittag-Leffler function and associated fractional calculus operators." Georgian Mathematical Journal 27, no. 2 (2020): 199–209. http://dx.doi.org/10.1515/gmj-2019-2030.

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AbstractMotivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function. We then systematically investigate several properties of the extended Mittag-Leffler function including some basic properties, Mellin, Euler-Beta, Laplace and Whittaker transforms. Furt

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36

Naz, Adiba, Sumit Nagpal, and V. Ravichandran. "Geometric Properties of Generalized Bessel Function Associated with the Exponential Function." Mathematica Slovaca 73, no. 6 (2023): 1459–78. http://dx.doi.org/10.1515/ms-2023-0106.

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ABSTRACT Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind, which is an elementary transform of the hypergeometric function and other related functions belong to subclasses of starlike and convex functions defined in the unit disk associated with the exponential mapping. Several differential subordination implications are derived for analytic functions involving Bessel function and the operator introduced by Baricz et al. [Differential subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci.

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37

Zhang, Yanyan, Ghulam Farid, Zabidin Salleh, and Ayyaz Ahmad. "On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator." Mathematical Problems in Engineering 2021 (October 13, 2021): 1–9. http://dx.doi.org/10.1155/2021/6043769.

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The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fra

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38

Agarwal, Praveen, Junesang Choi, Shilpi Jain, and Mohammad Mehdi Rashidi. "CERTAIN INTEGRALS ASSOCIATED WITH GENERALIZED MITTAG-LEFFLER FUNCTION." Communications of the Korean Mathematical Society 32, no. 1 (2017): 29–38. http://dx.doi.org/10.4134/ckms.c150247.

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39

Răducanu, Dorina. "Differential subordination associated with generalized Mittag-Leffler function." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 2 (2018): 435–52. http://dx.doi.org/10.1007/s13398-017-0487-3.

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40

Steuding, Jörn, and Ade Irma Suriajaya. "Mean-values associated with a generalized Schemmel function." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 54 (2023): 307–19. https://doi.org/10.71352/ac.54.307.

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We prove mean-value results for Schemmel's function (generalizing Euler's totient function). This function was originally defined to count the number of sets of m consecutive integers each being leq n and coprime to n. We generalize this to all integers m and consider its various mean-values.

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41

Nikolaev, Oleksii, and Alina Krainychenko. "ELASTIC TRANSVERSAL-ISOTROPIC SPACE WITH TWO UNIAXIAL PARALLEL CIRCULAR CRACKS AND ASSOCIATED PROBLEMS OF BASICITY." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (April 13, 2023): 92–105. http://dx.doi.org/10.20998/2222-0631.2022.01.11.

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In the paper a problem of the stress state in a transversely isotropic space with two parallel circular cracks, the centers of which are located on the axis of anisotropy of the space, is investigated. A constant normal load acts on the crack planes. The problem is solved by the generalized Fourier method. For this purpose, systems of compressed spheroidal coordinates are introduced, the origins of which are connected to the centers of cracks. The general solution of the problem is constructed in the form of series based on axisymmetric variants of the general vector solutions of the system of

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42

Ayant, Frederic. "Contour Integrals Involving Generalized Associated Function and Generalzed Multivariable Gimel-Function." International Journal of Mathematics Trends and Technology 59, no. 3 (2018): 191–201. http://dx.doi.org/10.14445/22315373/ijmtt-v59p529.

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43

Secelean, Adrian. "Generalized countable iterated function systems." Filomat 25, no. 1 (2011): 21–36. http://dx.doi.org/10.2298/fil1101021s.

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One of the most common and most general way to generate fractals is by using iterated function systems which consists of a finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X ? X into X instead of contractions on the metric space X to itself, where (X, d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the

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44

Panwar, Savita, Prakriti Rai, and Rupakshi Mishra Pandey. "A new generalized beta function associated with statistical distribution and fractional kinetic equation." Boletim da Sociedade Paranaense de Matemática 42 (May 23, 2024): 1–15. http://dx.doi.org/10.5269/bspm.63031.

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Several authors have extensively investigated beta function, hypergeometric function and confluent hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and science. The main purpose of this paper is to present a new generalization of extended beta function, hypergeometric function and confluent hypergeometric function with the help of m-parameter Mittag-Leffler function, as well as examine some important properties like integral representations, differential formula and summation formulas. We also examin

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45

Altay, Gülay, and M. Cengİz Dökmecİ. "On the equations governing the motion of an anisotropic poroelastic material." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2072 (2006): 2373–96. http://dx.doi.org/10.1098/rspa.2006.1665.

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We address Biot's equations governing the motion of an anisotropic fluid-saturated poroelastic material with certain properties. First, we investigate the uniqueness in solutions of the three-dimensional governing equations for the regular region of the poroelastic material and enumerate the conditions sufficient for the uniqueness. Next, by applying Hamilton's principle to the motion of the region, we obtain a variational principle that generates only the Biot–Newton equations and the associated natural boundary conditions. Then, by extending the variational principle for the region with an i

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46

Rahman, Gauhar, Abdus Saboor, Zunaira Anjum, Kottakkaran Sooppy Nisar, and Thabet Abdeljawad. "An Extension of the Mittag-Leffler Function and Its Associated Properties." Advances in Mathematical Physics 2020 (September 22, 2020): 1–8. http://dx.doi.org/10.1155/2020/5792853.

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Inspired by certain fascinating ongoing extensions of the special functions such as an extension of the Pochhammer symbol and generalized hypergeometric function, we present a new extension of the generalized Mittag-Leffler (ML) function εa,b;p,vκz1 in terms of the generalized Pochhammer symbol. We then deliberately find certain various properties and integral transformations of the said function εa,b;p,vκz1. Some particular cases and outcomes of the main results are also established.

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Jun Chang, Seung, and Jae Gil Choi. "Generalized transforms and generalized convolution products associated with Gaussian paths on function space." Communications on Pure & Applied Analysis 19, no. 1 (2020): 371–89. http://dx.doi.org/10.3934/cpaa.2020019.

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Mohsen, Fadhle B. F., and Maisoon A. H. Kulib. "Obtaining generating relations associated with the generalized Gauss hypergeometric function." University of Aden Journal of Natural and Applied Sciences 22, no. 1 (2018): 151–57. http://dx.doi.org/10.47372/uajnas.2018.n1.a12.

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In this paper, some new generating relations involving the generalized hyper- geometric function and the generalized confluent hypergeometric function are established by mainly applying Taylor's Theorem. Due to their very general nature, the main results can be shown to be specialized to yield a large number of new, known, interesting and useful generating relations involving the Gauss hypergeometric function and its related functions.

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Mimachi, Katsuhisa. "Connection Matrices Associated with the Generalized Hypergeometric Function 3F2." Funkcialaj Ekvacioj 51, no. 1 (2008): 107–33. http://dx.doi.org/10.1619/fesi.51.107.

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Sebastian, Nicy. "A generalized gamma model associated with a Bessel function." Integral Transforms and Special Functions 22, no. 9 (2011): 631–45. http://dx.doi.org/10.1080/10652469.2010.536413.

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