Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampe de Feriet functions

被引：13

作者：

Greynat, David ^{[1
]}

Sesma, Javier ^{[2
]}

Vulvert, Gregory ^{[3
]}

机构：

[1] Ist Nazl Fis Nucl, Dipartimento Fis, Sez Napoli, I-80126 Naples, Italy

[2] Univ Zaragoza, Fac Ciencias, Dept Fis Teor, E-50009 Zaragoza, Spain

[3] Univ Valencia, CSIC, Dept Fis Teor, IFIC, E-46071 Valencia, Spain

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2014年 / 55卷 / 04期

关键词：

EXPANDING HYPERGEOMETRIC-FUNCTIONS; TRANSCENDENTAL FUNCTIONS; GENERALIZED BERNOULLI; BINOMIAL SUMS; SERIES;

D O I：

10.1063/1.4870619

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Useful expressions of the derivatives, to any order, of Pochhammer and reciprocal Pochhammer symbolswith respect to their arguments are presented. They are building blocks of a procedure, recently suggested, for obtaining the e-expansion of functions of the hypergeometric class related to Feynman integrals. The procedure is applied to some examples of such kind of functions taken from the literature. (C) 2014 AIP Publishing LLC.

引用

页数：16

共 5 条

[1] APPELL-KAMPE DE FERIET HYPERGEOMETRIC-FUNCTIONS OF 2 VARIABLES
GOLUBEVA, VA
SIBERIAN MATHEMATICAL JOURNAL, 1979, 20 (05) : 705 - 717
[2] Ordinary and basic bivariate hypergeometric transformations associated with the Appell and Kampe de Feriet functions
Chu, WC
Srivastava, HM
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 156 (02) : 355 - 370
[3] A NOTE ON CERTAIN TRANSFORMATION FORMULAS RELATED TO APPELL, HORN AND KAMPE DE FERIET FUNCTIONS
Mohammed, Asmaa Orabi
Rakha, Medhat Ahmed
Rathie, Arjun K.
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2023, 38 (03): : 807 - 819
[4] RELATIONS BETWEEN THE HYPERGEOMETRIC FUNCTION OF APPELL F3 AND KAMPE DE FERIET FUNCTIONS
Choi, Junesang
Kim, Yong Sup
Hasanov, Anvar
MISKOLC MATHEMATICAL NOTES, 2011, 12 (02) : 131 - 148
[5] When presenting to the Academy a volume entitled Hypergeometric and Hyperspheric Functions; Hermite's polynomials, which he wrote in collaboration with M. Kampe de Feriet, a lecturer at the Lille University, M. P. Appell said
Appell, P
De Feriet, K
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1926, 183 : 176 - 177

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