APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

被引：5

作者：

Srivastava, H. M. ^{[1
]}

Qureshi, M. I. ^{[2
]}

Quraishi, Kaleem A. ^{[3
]}

Arora, Ashish ^{[4
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] Jamia Millia Islamia, Fac Engn & Technol, Dept Appl Sci & Humanities, New Delhi 110025, India

[3] Mewat Engn Coll Wakf, Sect Math, Mewat 122107, Haryana, India

[4] Noida Inst Engn & Technol, Dept Math, Gautambuddha Nagar 201306, Uttar Pradesh, India

来源：

ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 03期

关键词：

Pochhammer's symbol; Gamma function; series identities; hypergeometric reduction formulas; Srivastava-Daoust double and multiple hypergeometric functions; Legendre's duplication formula; Gauss-Legendre multiplication formula; Kummer's theorem; Dixon's theorem; IDENTITIES;

D O I：

10.1016/S0252-9602(14)60034-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

引用

页码：619 / 628

页数：10

共 50 条

[21] Summation formulae for elliptic hypergeometric series
Warnaar, SO
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (02) : 519 - 527
[22] A STUDY OF GENERALIZED SUMMATION THEOREMS FOR THE SERIES 2F1 WITH AN APPLICATIONS TO LAPLACE TRANSFORMS OF CONVOLUTION TYPE INTEGRALS INVOLVING KUMMER'S FUNCTIONS 1F1
Milovanovic, Gradimir V.
Parmar, Rakesh K.
Rathie, Arjun K.
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2018, 12 (01) : 257 - 272
[23] Summation identities and transformations for hypergeometric series
Barman R.
Saikia N.
Annales mathématiques du Québec, 2018, 42 (2) : 133 - 157
[24] Characterization of Kummer hypergeometric Bernoulli polynomials and applications
Drissi, Driss
COMPTES RENDUS MATHEMATIQUE, 2019, 357 (10) : 743 - 751
[25] pi AND OTHER FORMULAE IMPLIED BY HYPERGEOMETRIC SUMMATION THEOREMS
Kim, Yong Sup
Rathie, Arjun Kumar
Wang, Xiaoxia
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 30 (03): : 227 - 237
[26] Note on the Dixon formula for a finite hypergeometric series
Brown, BM
Eastham, MSP
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) : 173 - 175
[27] APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES 2F1
Kim, Yong Sup
Rathie, Arjun K.
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (06) : 1201 - 1211
[28] Applications of Extended Kummer's Summation Theorem
Wang, Xiaoxia
Rathie, Arjun K.
Lim, Eunyoung
Kim, Hwajoon
MATHEMATICS, 2024, 12 (19)
[29] COMPARATIVE THEOREMS ON SUMMATION PROPERTIES OF CESARO METHOD RELATED TO DOUBLE SERIES
GARCET, A
BULLETIN DE LA CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE, 1970, 56 (01): : 38 - &
[30] THE SUMMATION OF SERIES INVOLVING ROOTS OF TRANSCENDENTAL EQUATIONS AND RELATED APPLICATIONS
SPEIGEL, MR
JOURNAL OF APPLIED PHYSICS, 1953, 24 (09) : 1103 - 1106

← 1 2 3 4 5 →