Hypergeometric series summations and π-formulas

被引：1

作者：

Liu, Hongmei ^{[1
]}

机构：

[1] Dalian Nationalities Univ, Sch Sci, Dalian 116600, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 419卷 / 01期

关键词：

Hypergeometric summation formulas; Ramanujan-type series; RAMANUJAN-TYPE SERIES; 1/PI;

D O I：

10.1016/j.jmaa.2014.04.071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By two Slater's hypergeometric series identities, we establish two general summation formulas with six free parameters. Specializing certain parameters in these formulas, we obtain a list of Ramanujan-type series formulas for pi, pi(2) and pi(3). (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：553 / 561

页数：9

共 50 条

[41] NUMERICAL EVALUATION OF THE GAUSS HYPERGEOMETRIC FUNCTION BY POWER SUMMATIONS
Doornik, Jurgen A.
MATHEMATICS OF COMPUTATION, 2015, 84 (294) : 1813 - 1833
[42] On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences
Bakhtin, Kirill
Prilepkina, Elena
MATHEMATICS, 2024, 12 (11)
[43] New algorithms for deriving reduction formulas for hypergeometric series of multiple variables
O. S. Paramonova
A. V. Niukkanen
Programming and Computer Software, 2000, 26 : 42 - 43
[44] RECURSION FORMULAS FOR q-HYPERGEOMETRIC AND q-APPELL SERIES
Sahai, Vivek
Verma, Ashish
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 33 (01): : 207 - 236
[45] Reduction Formulas for Generalized Hypergeometric Series Associated with New Sequences and Applications
Choi, Junesang
Qureshi, Mohd Idris
Bhat, Aarif Hussain
Majid, Javid
FRACTAL AND FRACTIONAL, 2021, 5 (04)
[46] SOME TRANSFORMATION AND REDUCTION FORMULAS FOR HYPERGEOMETRIC-SERIES IN SEVERAL VARIABLES
GROSJEAN, CC
SRIVASTAVA, HM
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1991, 37 (1-3) : 287 - 299
[47] Computer generation of complicated transformations and reduction formulas for multiple hypergeometric series
Niukkanen, AW
Paramonova, OS
COMPUTER PHYSICS COMMUNICATIONS, 2000, 126 (1-2) : 141 - 148
[48] SOME QUADRATIC AND CUBIC SUMMATION FORMULAS FOR BASIC HYPERGEOMETRIC-SERIES
RAHMAN, M
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1993, 45 (02): : 394 - 411
[49] Duality Transformation Formulas for Multiple Elliptic Hypergeometric Series of Type BC
Komori, Yasushi
Masuda, Yasuho
Noumi, Masatoshi
CONSTRUCTIVE APPROXIMATION, 2016, 44 (03) : 483 - 516
[50] New algorithms for deriving reduction formulas for hypergeometric series of multiple variables
Paramonova, OS
Niukkanen, AV
PROGRAMMING AND COMPUTER SOFTWARE, 2000, 26 (01) : 42 - 43

← 1 2 3 4 5 →