Relevant bibliographies by topics / Generalized associated Legendre function of first kind

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Academic literature on the topic 'Generalized associated Legendre function of first kind'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Generalized associated Legendre function of first kind"

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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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Szmytkowski, Radosław, and Sebastian Bielski. "A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices." Integral Transforms and Special Functions 25, no. 4 (2013): 312–17. http://dx.doi.org/10.1080/10652469.2013.842235.

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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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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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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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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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Schmidt, Maxie D. "Zeta series generating function transformations related to generalized Stirling numbers and partial sums of the Hurwitz zeta function." Online Journal of Analytic Combinatorics, no. 13 (December 31, 2018): 1–31. https://doi.org/10.61091/ojac-1303.

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We define a generalized class of modified zeta series transformations generating the partial sums of the Hurwitz zeta function and series expansions of the Lerch transcendent function. The new transformation coefficients we define within the article satisfy expansions by generalized harmonic number sequences as the partial sums of the Hurwitz zeta function. These transformation coefficients satisfy many properties which are analogous to known identities and expansions of the Stirling numbers of the first kind and to the known transformation coefficients employed to enumerate variants of the po
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Szmytkowski, Radosław. "On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)." Journal of Mathematical Analysis and Applications 386, no. 1 (2012): 332–42. http://dx.doi.org/10.1016/j.jmaa.2011.08.003.

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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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Cho, Nak, Hyo Lee, and Rekha Srivastava. "Characterizations for certain subclasses of starlike and convex functions associated with Bessel functions." Filomat 30, no. 7 (2016): 1911–17. http://dx.doi.org/10.2298/fil1607911c.

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In the present paper, we obtain some characterizations for a certain generalized Bessel function of the first kind to be in the subclasses SpT(?,?), UCT(?,?), PT(?) and CPT(?) of normalized analytic functions in the open unit disk U. Furthermore, we consider an integral operator related to the generalized Bessel Function which we have characterized here.
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Book chapters on the topic "Generalized associated Legendre function of first kind"

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Fukushima, Toshio. "Numerical Computation of Point Values, Derivatives, and Integrals of Associated Legendre Function of the First Kind and Point Values and Derivatives of Oblate Spheroidal Harmonics of the Second Kind of High Degree and Order." In International Association of Geodesy Symposia. Springer International Publishing, 2015. http://dx.doi.org/10.1007/1345_2015_124.

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"Integral representations of the generalized associated Legendre functions of the first kind." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0009.

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"Dual integral equations with the generalized Legendre function of the first kind $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0016.

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"Triple integral equations with the generalized Legendre function of the first kind $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0018.

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"Systems of triple integral equations with the generalized associated Legendre functions of the first kind $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0020.

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