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Journal articles on the topic 'Joseph Kampé de Fériet'

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Published: 4 June 2021

Last updated: 13 February 2022

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1

Demuro, Antonietta. "Joseph Kampé de Fériet et la mécanique des fluides en France durant l'entre-deux-guerres." Comptes Rendus Mécanique 345, no. 8 (2017): 556–69. http://dx.doi.org/10.1016/j.crme.2017.05.013.

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2

Hwang, Kyung-Won, Young-Soo Seol, and Cheon-Seoung Ryoo. "Explicit Identities for 3-Variable Degenerate Hermite Kampé de Fériet Polynomials and Differential Equation Derived from Generating Function." Symmetry 13, no. 1 (2020): 7. http://dx.doi.org/10.3390/sym13010007.

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We get the 3-variable degenerate Hermite Kampé de Fériet polynomials and get symmetric identities for 3-variable degenerate Hermite Kampé de Fériet polynomials. We make differential equations coming from the generating functions of degenerate Hermite Kampé de Fériet polynomials to get some identities for 3-variable degenerate Hermite Kampé de Fériet polynomials,. Finally, we study the structure and symmetry of pattern about the zeros of the 3-variable degenerate Hermite Kampé de Fériet equations.

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3

Verma, Ashish, Jihad Younis, and Hassen Aydi. "On the Kampé de Fériet Hypergeometric Matrix Function." Mathematical Problems in Engineering 2021 (August 18, 2021): 1–11. http://dx.doi.org/10.1155/2021/9926176.

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In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function.

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4

Ernst, Thomas. "Decomposition Formulas for Triple q-Hypergeometric Functions." International Journal of Combinatorics 2014 (May 15, 2014): 1–14. http://dx.doi.org/10.1155/2014/712321.

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In the spirit of Hasanov, Srivastava, and Turaev (2006), we introduce new inverse operators together with a more general operator and find a summation formula for the last one. Based on these operators and the earlier known q-analogues of the Burchnall-Chaundy operators, we find 15 symbolic operator formulas. Then, 10 expansions for the q-analogues of Srivastava’s three triple hypergeometric functions in terms of ϕ34q-hypergeometric and q-Kampé de Fériet functions are derived. These expansions readily reduce to 10 new expansions for the three triple Srivastava hypergeometric functions in terms

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5

Kim, Yong-Sup, Shoukat Ali, and Navratna Rathie. "GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION." Honam Mathematical Journal 33, no. 1 (2011): 43–50. http://dx.doi.org/10.5831/hmj.2011.33.1.043.

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6

Choi, Junesang, and Arjun K. Rathie. "ON THE REDUCIBILITY OF KAMPÉ DE FÉRIET FUNCTION." Honam Mathematical Journal 36, no. 2 (2014): 345–55. http://dx.doi.org/10.5831/hmj.2014.36.2.345.

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7

Exton, Harold. "Transformation of certain generalized Kampé de Fériet functions." Journal of Physics A: Mathematical and General 29, no. 2 (1996): 357–63. http://dx.doi.org/10.1088/0305-4470/29/2/016.

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8

ALI, SHOUKAT. "A TRANSFORMATION FORMULA FOR THE KAMPÉ DE FÉRIET FUNCTION." International Journal of Modern Physics: Conference Series 22 (January 2013): 713–19. http://dx.doi.org/10.1142/s2010194513010908.

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In 1997, Exton have obtained an interesting case of the transformation of Kampé de Fériet function by employing classical Watson’s theorem on the sum of a 3F2 . The aim of this research note is to obtain one result contiguous to that of Exton.

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9

Marko, Dashrath Singh. "Generalized Single Integral Involving Multivariable Kampé De Fériet Function." IOSR Journal of Mathematics 8, no. 6 (2013): 67–70. http://dx.doi.org/10.9790/5728-0866770.

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10

Liu, Hongmei, and Weiping Wang. "Transformation and summation formulae for Kampé de Fériet series." Journal of Mathematical Analysis and Applications 409, no. 1 (2014): 100–110. http://dx.doi.org/10.1016/j.jmaa.2013.06.068.

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11

Rakha, Medhat A., Mohammed M. Awad, and Arjun K. Rathie. "On a reducibility of the Kampé de Fériet function." Mathematical Methods in the Applied Sciences 38, no. 12 (2014): 2600–2605. http://dx.doi.org/10.1002/mma.3245.

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12

Exton, Harold. "Transformations of certain generalized Kampé de Fériet functions II." Journal of Applied Mathematics and Stochastic Analysis 10, no. 3 (1997): 297–304. http://dx.doi.org/10.1155/s1048953397000373.

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The development of identities of multivariable hypergeometric functions is further extended based upon the methods of the previous study (H. Exton, J. Phys. A29 (1996), 357-363) these functions occur in various applications in the fields of physics and quantum chemistry.

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13

Zayed, Ahmed I. "Construction of orthonormal wavelets using Kampé de Fériet functions." Proceedings of the American Mathematical Society 130, no. 10 (2002): 2893–904. http://dx.doi.org/10.1090/s0002-9939-02-06690-x.

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14

Cvijović, Djurdje, and Allen R. Miller. "A reduction formula for the Kampé de Fériet function." Applied Mathematics Letters 23, no. 7 (2010): 769–71. http://dx.doi.org/10.1016/j.aml.2010.03.006.

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15

Cassisa, C., P. E. Ricci, and I. Tavkhelidze. "Operational Identities for Circular and Hyperbolic Functions and Their Generalizations." Georgian Mathematical Journal 10, no. 1 (2003): 45–56. http://dx.doi.org/10.1515/gmj.2003.45.

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Abstract Starting from the exponential, some classes of analytic functions of the derivative operator are studied, including pseudo-hyperbolic and pseudo-circular functions. Some formulas related to operational calculus are deduced, and the important role played in such a context by Hermite–Kampé de Fériet polynomials is underlined.

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16

Verma, Ashish, Jihad Younis, Vikash Kumar Pandey, and Hassen Aydi. "Some Summation Formulas for the Generalized Kampé de Fériet Function." Mathematical Problems in Engineering 2021 (September 15, 2021): 1–11. http://dx.doi.org/10.1155/2021/2861820.

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The aim of this manuscript is to establish several finite summation formulas (FSFs) for the generalized Kampé de Fériet series (GKDFS). Moreover, the particular result for confluent forms of Lauricella series in n variables and four generalized Lauricella functions are obtained from the finite summation formulas for the GKDFS.

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17

Sahai, Vivek, and Ashish Verma. "nth-Order q-derivatives of multivariable q-hypergeometric series with respect to parameters." Asian-European Journal of Mathematics 07, no. 02 (2014): 1450019. http://dx.doi.org/10.1142/s1793557114500193.

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We obtain nth-order q-derivatives of certain multivariable q-hypergeometric series with respect to parameters. We consider fourteen 3-variable q-Lauricella series, four k-variable q-Lauricella series and the generalized q-Kampé de Fériet series for this purpose. Some relations between q-derivatives of these series with respect to parameters and variables are also given.

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18

Lavoie, J. L., and F. Grondin. "The Kampé de Fériet Functions: A Family of Reduction Formulas." Journal of Mathematical Analysis and Applications 186, no. 2 (1994): 393–401. http://dx.doi.org/10.1006/jmaa.1994.1307.

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19

Miller, A. R., and R. B. Paris. "A Generalised Kummer-Type Transformation for the pFp(x) Hypergeometric Function." Canadian Mathematical Bulletin 55, no. 3 (2012): 571–78. http://dx.doi.org/10.4153/cmb-2011-095-6.

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AbstractIn a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p = 1.

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20

Oda, Takayuki. "Matrix coefficients of the large discrete series representations of Sp(2; R) as hypergeometric series of two variables." Nagoya Mathematical Journal 208 (December 2012): 201–63. http://dx.doi.org/10.1017/s0027763000010631.

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AbstractWe investigate the radial part of the matrix coefficients with minimal K-types of the large discrete series representations of Sp(2; R). They satisfy certain difference-differential equations derived from Schmid operators. This system is reduced to a holonomic system of rank 4, which is finally found to be equivalent to higher-order hypergeometric series in the sense of Appell and Kampé de Fériet.

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21

Chu, W., and W. Zhang. "Well-posed reduction formulas for the q-Kampé-de-Fériet function." Ukrainian Mathematical Journal 62, no. 11 (2011): 1783–802. http://dx.doi.org/10.1007/s11253-011-0468-1.

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22

Ernst, Thomas, and Per W. Karlsson. "Corollaries and multiple extensions of Gessel and Stanton hypergeometric summation formulas." Acta et Commentationes Universitatis Tartuensis de Mathematica 25, no. 1 (2021): 21–31. http://dx.doi.org/10.12697/acutm.2021.25.02.

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We find some new simple hypergeometric formulas in the footsteps of the important article by Gessel and Stanton. These are multiple reduction formulas, multiple summation formulas, as well as multiple transformation formulas for special Kampé de Fériet functions and Appell functions. The hypergeometric summation formulas have special function arguments in Q and parameter values in N or C. The proofs use Pfaff-Kummer transformation, Euler transformation, or an improved form of Slater reversion.

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23

Bretti, Gabriella, Pierpaolo Natalini, and Paolo E. Ricci. "Generalizations of the Bernoulli and Appell polynomials." Abstract and Applied Analysis 2004, no. 7 (2004): 613–23. http://dx.doi.org/10.1155/s1085337504306263.

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We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.

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24

Pitre, S. N., and J. Van der Jeugt. "Transformation and Summation Formulas for Kampé de Fériet SeriesF0:31:1(1,1)." Journal of Mathematical Analysis and Applications 202, no. 1 (1996): 121–32. http://dx.doi.org/10.1006/jmaa.1996.0306.

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25

Choi, Junesang, Yong Sup Kim, and Anvar Hasanov. "Relations between hypergeometric function of Appel $F_3$ and Kampé de Fériet functions." Miskolc Mathematical Notes 12, no. 2 (2011): 131. http://dx.doi.org/10.18514/mmn.2011.312.

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26

Miller, Allen R. "Reduction formulae for Kampé de Fériet functions Fq:1; 0p:2; 1." Journal of Mathematical Analysis and Applications 151, no. 2 (1990): 428–37. http://dx.doi.org/10.1016/0022-247x(90)90158-c.

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27

Chu, Wenchang, and Nadia N. Li. "Reduction and summation formulae for semi-terminating q-Kampé de Fériet series." Afrika Matematika 24, no. 4 (2012): 647–64. http://dx.doi.org/10.1007/s13370-012-0085-7.

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28

Agarwal, Praveen, and Mehar Chand. "Graphical Analysis of Kampé De Fériet's Series with Implementation of MATLAB." International Journal of Computer Applications 59, no. 4 (2012): 1–10. http://dx.doi.org/10.5120/9533-3966.

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29

Sunil Pandey, Sunil Pandey. "Expansion Formulae for Generalized Kampé De Fériet Function, Radial Wave Functios And Heat Conduction." IOSR Journal of Mathematics 5, no. 3 (2013): 25–29. http://dx.doi.org/10.9790/5728-0532529.

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30

COFFEY, MARK W. "ON HYPERGEOMETRIC SERIES REDUCTIONS FROM INTEGRAL REPRESENTATIONS, THE KAMPÉ DE FÉRIET FUNCTION AND ELSEWHERE." International Journal of Modern Physics B 19, no. 30 (2005): 4483–93. http://dx.doi.org/10.1142/s0217979205032814.

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Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrödinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1Fp, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.

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31

Gade, R. M. "q2-Kampé de Fériet series and sums of continuous dual q±2-Hahn polynomials." Journal of Mathematical Physics 52, no. 6 (2011): 063519. http://dx.doi.org/10.1063/1.3592599.

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32

Chu, Wen-Chang, and H. M. Srivastava. "Ordinary and basic bivariate hypergeometric transformations associated with the Appell and Kampé de Fériet functions." Journal of Computational and Applied Mathematics 156, no. 2 (2003): 355–70. http://dx.doi.org/10.1016/s0377-0427(02)00921-4.

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33

Abd-Elhameed, Waleed Mohamed, and Afnan Ali. "New Specific and General Linearization Formulas of Some Classes of Jacobi Polynomials." Mathematics 9, no. 1 (2020): 74. http://dx.doi.org/10.3390/math9010074.

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The main purpose of the current article is to develop new specific and general linearization formulas of some classes of Jacobi polynomials. The basic idea behind the derivation of these formulas is based on reducing the linearization coefficients which are represented in terms of the Kampé de Fériet function for some particular choices of the involved parameters. In some cases, the required reduction is performed with the aid of some standard reduction formulas for certain hypergeometric functions of unit argument, while, in other cases, the reduction cannot be done via standard formulas, so

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34

Miller, Allen R. "Reductions of a Generalized Incomplete Gamma Function, Related Kampé de Fériet Functions, and Incomplete Weber Integrals." Rocky Mountain Journal of Mathematics 30, no. 2 (2000): 703–14. http://dx.doi.org/10.1216/rmjm/1022009290.

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35

Ancarani, L. U., and G. Gasaneo. "A special asymptotic limit of a Kampé de Fériet hypergeometric function appearing in nonhomogeneous Coulomb problems." Journal of Mathematical Physics 52, no. 2 (2011): 022108. http://dx.doi.org/10.1063/1.3554698.

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36

Miller, A. R., and H. M. Srivastava. "Further reducible cases of certain Kampé de Fériet functions associated with incomplete integrals of cylindrical functions." Applied Mathematics and Computation 68, no. 2-3 (1995): 199–216. http://dx.doi.org/10.1016/0096-3003(94)00094-k.

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37

Ryoo, Cheon. "Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros." Mathematics 7, no. 1 (2018): 23. http://dx.doi.org/10.3390/math7010023.

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In this paper, we study differential equations arising from the generating functions of Hermit Kamp e ´ de F e ´ riet polynomials. Use this differential equation to give explicit identities for Hermite Kamp e ´ de F e ´ riet polynomials. Finally, use the computer to view the location of the zeros of Hermite Kamp e ´ de F e ´ riet polynomials.

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38

Juršėnas, Rytis. "On the definite integral of two confluent hypergeometric functions related to the Kampé de Fériet double series." Lithuanian Mathematical Journal 54, no. 1 (2014): 61–73. http://dx.doi.org/10.1007/s10986-014-9227-y.

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39

Sahai, Vivek, and Ashish Verma. "Recursion formulas for the Srivastava–Daoust and related multivariable hypergeometric functions." Asian-European Journal of Mathematics 09, no. 04 (2016): 1650081. http://dx.doi.org/10.1142/s1793557116500819.

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This paper concludes the study of recursion formulas of multivariable hypergeometric functions. Earlier in [V. Sahai and A. Verma, Recursion formulas for multivariable hypergeometric functions, Asian–Eur. J. Math. 8 (2015) 50, 1550082], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava’s triple hypergeometric functions and [Formula: see text]-variable Lauricella functions. Further, in [V. Sahai and A. Verma, Recursion formulas for Recursion formulas for Srivastava’s general triple hypergeometric functions, Asian–Eur. J. Math. 9 (2016) 17, 1650063

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40

Choi, Junesang, and Arjun Rathie. "Reducibility of certain Kampé de Fériet function with an application to generating relations for products of two Laguerre polynomials." Filomat 30, no. 7 (2016): 2059–66. http://dx.doi.org/10.2298/fil1607059c.

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It has been an interesting and natural research subject to consider the reducibility of some extensively generalized special functions. In this regard, Kamp? de F?riet function has been attracted by many mathematicians. The authors [7] also established many interesting cases of the reducibility of Kamp? de F?riet function by employing generalizations of the two results for the terminating 2F1(2) hypergeometric identities due to Kim et al. In this sequel, we first aim at presenting several interesting cases of the reducibility of Kamp? de F?riet function by using generalizations of classical Ku

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41

Miller, A. R., and H. M. Srivastava. "Reduction formulas for kampé de Fériet functions associated with certain classes of incomplete Lipschitz—Hankel type integrals of cylindrical functions." Journal of the Franklin Institute 329, no. 1 (1992): 155–70. http://dx.doi.org/10.1016/0016-0032(92)90105-p.

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42

Chu, Wenchang, and Nadia N. Li. "Terminating $q$-Kampé de Fériet Series $\Phi^{1:3;\lam}_{1:2;\mu}$ and $\Phi^{2:2;\lam}_{2:1;\mu}$." Hiroshima Mathematical Journal 42, no. 2 (2012): 233–52. http://dx.doi.org/10.32917/hmj/1345467072.

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43

Greynat, David, Javier Sesma, and Grégory Vulvert. "Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions." Journal of Mathematical Physics 55, no. 4 (2014): 043501. http://dx.doi.org/10.1063/1.4870619.

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44

Santander, J. L. G. "A Note on Some Reduction Formulas for the Generalized Hypergeometric Function $$_{2}F_{2}$$ 2 F 2 and Kampé de Fériet Function." Results in Mathematics 71, no. 3-4 (2017): 949–54. http://dx.doi.org/10.1007/s00025-017-0654-z.

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45

Savischenko, N. V., and E. V. Lebeda. "Multi-position signal coherent reception error probability in a channel with generalized gamma or K fading and white noise." Information and Control Systems, no. 1 (February 19, 2019): 76–88. http://dx.doi.org/10.31799/1684-8853-2019-1-76-88.

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Introduction:One of the main problems in communication theory is giving definitions to such characteristics of an information transmission system as noise immunity (error probability) and transfer rate. Their knowledge allows you to determine the transmitted information quality and quantity, respectively. The calculation of the error probability for a communications channel (for example, with fading) allows you to estimate the loss or gain in noise immunity with modems of various signal designs.Purpose:Developing a technique for calculating the probability of a bit error with coherent receptio

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46

"On the integration of incomplete elliptic integrals." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 444, no. 1922 (1994): 525–32. http://dx.doi.org/10.1098/rspa.1994.0036.

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We give a closed-form evaluation of Erdélyi-Kober fractional integrals, involving incomplete elliptic integrals of the first kind, F ( φ, k ), and of the second kind, E ( φ, k ), which are integrated either with respect to the modulus or the amplitude. This is made possible by representing F ( φ, k ) and E ( φ, k ) in terms of the Kampé de Fériet double hypergeometric functions. Reduction formulae for these enable us to simplify the solutions for thirteen special cases, including integrals involving complete elliptic integrals. The hypergeometric character of the incomplete integrals is useful

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47

Fortin, Jean-François, Wen-Jie Ma, and Witold Skiba. "Six-point conformal blocks in the snowflake channel." Journal of High Energy Physics 2020, no. 11 (2020). http://dx.doi.org/10.1007/jhep11(2020)147.

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Abstract We compute d-dimensional scalar six-point conformal blocks in the two possible topologies allowed by the operator product expansion. Our computation is a simple application of the embedding space operator product expansion formalism developed recently. Scalar six-point conformal blocks in the comb channel have been determined not long ago, and we present here the first explicit computation of the scalar six-point conformal blocks in the remaining inequivalent topology. For obvious reason, we dub the other topology the snowflake channel. The scalar conformal blocks, with scalar externa

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48

Ananthanarayan, B., Samuel Friot, and Shayan Ghosh. "Three-loop QED contributions to the g−2 of charged leptons with two internal fermion loops and a class of Kampé de Fériet series." Physical Review D 101, no. 11 (2020). http://dx.doi.org/10.1103/physrevd.101.116008.

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