A cubic transformation formula for 2F1(1/3, 2/3; 1; z) and some arithmetic convolution formulae

被引：9

作者：

Williams, KS ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ctr Res Algebra & Number Theory, Ottawa, ON K1S 5B6, Canada

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2004年 / 137卷

关键词：

D O I：

10.1017/S0305004104007832

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A cubic transformation formula for the hypergeometric function F-2(1) (1/3, 2/3; 1; z) is proved. As an application of this formula a number of arithmetic convolution sums are evaluated. For example, Melfi's formula, [GRAPHICS] is proved without the use of modular forms.

引用

页码：519 / 539

页数：21

共 50 条

[21] The Gauss 2F1(1)-summation theorem and harmonic number identities
Chen, Xiaojing
Chu, Wenchang
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2009, 20 (12) : 925 - 935
[22] New summation formula for 3F2(1/2) and a Kummer-type II transformation of 2F2(x)
Rathie, Arjun K.
Pogany, Tibor K.
MATHEMATICAL COMMUNICATIONS, 2008, 13 (01) : 63 - 66
[23] Hybridization effects in some UTSi (2:1:3;1:1:1;2:3:1) compounds
Lupsa, I
Valeanu, M
MODERN PHYSICS LETTERS B, 2003, 17 (24): : 1277 - 1282
[24] Contiguous relations and their computations for 2F1 hypergeometric series
Ibrahim, Adel K.
Rakha, Medhat A.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (08) : 1918 - 1926
[25] The Feynman integral in R1 ⊕ Rm and complex expansion of 2F1
Shpot, Mykola A.
Pogany, Tibor K.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2016, 27 (07) : 533 - 547
[26] (Z)-2,3,2′,3′-Tetrahydro-[1,1′]biindenylidene
Jovanovic, J
Elling, W
Schürmann, M
Preut, H
Spiteller, M
ACTA CRYSTALLOGRAPHICA SECTION E-CRYSTALLOGRAPHIC COMMUNICATIONS, 2002, 58 : O35 - O36
[27] 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
[28] Generalized Watson's summation formula for 3F2(1)
Lewanowicz, S
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 86 (02) : 375 - 386
[29] The analytic continuation of the Gaussian hypergeometric function 2F1(a, b; c; z) for arbitrary parameters
Becken, W
Schmelcher, P
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 126 (1-2) : 449 - 478
[30] A transformation formula for the generalized hypergeometric series 4F3(1)
Miller, AR
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (47): : 11853 - 11858

← 1 2 3 4 5 →