Evaluations of some terminating hypergeometric 2F1(2)2F1(2)_2F_1(2) series with applications

Yong Sup KIM; Arjunkumar RATHIE; Richard B. PARIS

Article Details

Evaluations of some terminating hypergeometric 2F1(2)2F1(2)_2F_1(2) series with applications

Authors:

Yong Sup KIM | Arjunkumar RATHIE | Richard B. PARIS

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2563-2575

Document Type:

Article

Publication Date:

9/2018

Document Language:

Turkish

Document ID (Org No.):

2000745781

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

Explicit expressions for the hypergeometric series 2F1(−n,a;2a±j;2)2F1(−n,a;2a±j;2)_2F_1(-n, a; 2a\pm j;2) and 2F1(−n,a;−2n±j;2)2F1(−n,a;−2n±j;2)_2F_1(-n, a; -2n \pm j;2)  for positive integer nnn and arbitrary integer jjj 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|j|≤5|j|\leq 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)3F2(2)_3F_2(2) series and the confluent hypergeometric function  1F1(x)1F1(x)_1F_1(x).

Article Details

Evaluations of some terminating hypergeometric 2F1(2)2F1(2)_2F_1(2) series with applications

Authors: Yong Sup KIM | Arjunkumar RATHIE | Richard B. PARIS

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2563-2575

Document Type: Article

Publication Date: 9/2018

Document Language: Turkish

Document ID (Org No.): 2000745781

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Yong Sup KIM | Arjunkumar RATHIE | Richard B. PARIS

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2018 Vol.42 Issue 5, pp.2563-2575

Document Type:

Article

Publication Date:

9/2018

Document Language:

Turkish

Document ID (Org No.):

2000745781

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098