Evaluations of some terminating hypergeometric 2F1(2) series with applications

Yongsup Kim; Arjun Kumar Rathie; Richard Bruce Paris

doi:10.3906/mat-1804-67

Evaluations of some terminating hypergeometric ₂F₁(2) series with applications

Yongsup Kim^*, Arjun Kumar Rathie, Richard Bruce Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

180 Downloads (Pure)

Abstract

Explicit expressions for the hypergeometric series ₂F₁(-n, a; 2a±j; 2) and ₂F₁(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating ₃F₂(2) series and the confluent hypergeometric function ₁F₁(x).

Original language	English
Pages (from-to)	2563-2575
Number of pages	13
Journal	Turkish Journal of Mathematics
Volume	42
Issue number	5
DOIs	https://doi.org/10.3906/mat-1804-67
Publication status	Published - 27 Sept 2018

Keywords

Terminating hypergeometric series
Generalized Kummer’s second and third summation theorems

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Cite this

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title = "Evaluations of some terminating hypergeometric 2F1(2) series with applications",

abstract = "Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).",

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N2 - Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).

AB - Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).

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DO - 10.3906/mat-1804-67

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