scholarly journals Some new transformation formulas deriving from Bailey pairs and WP-Bailey pairs

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 941-953
Author(s):  
Shuyuan Nie ◽  
Zhizheng Zhang
Keyword(s):  
Hypergeometric Series ◽  
Bailey Pairs ◽  
Summation Formulas ◽  
Transformation Formulas

The purpose of this paper is to derive a new Bailey pair and three new WP-Bailey pairs from four summation formulas of the multibasic hypergeometric series. As applications, we will use them to obtain many new transformation formulas for basic and multibasic hypergeometric series.

scholarly journals A note on Bailey and WP-Bailey Pairs

2020 ◽  
Vol 5 (2) ◽  
pp. 143-156
Author(s):  
Satya Prakash Singh ◽  
Lakshmi Narayan Mishra ◽  
Vijay Yadav
Keyword(s):  
Hypergeometric Series ◽  
Bailey Pairs ◽  
Transformation Formulas

AbstractIn this paper, we have established certain theorems involving Bailey pairs and WP-Bailey pairs. Further, making use of some known WP-Bailey pairs and theorems for constructing new WP-Bailey pairs, we have also established transformation formulas for q-hypergeometric series.

scholarly journals Transformation formulas for terminating Saalschützian hypergeometric series of unit argument

1995 ◽  
Vol 8 (2) ◽  
pp. 189-194
Author(s):  
Wolfgang Bühring
Keyword(s):  
Recurrence Relation ◽  
Hypergeometric Series ◽  
Summation Formula ◽  
Summation Formulas ◽  
Finite Sums ◽  
Transformation Formulas ◽  
Independent Parameters

Transformation formulas for terminating Saalschützian hypergeometric series of unit argument p+1Fp(1) are presented. They generalize the Saalschützian summation formula for 3F2(1). Formulas for p=3,4,5 are obtained explicitly, and a recurrence relation is proved by means of which the corresponding formulas can also be derived for larger p. The Gaussian summation formula can be derived from the Saalschützian formula by a limiting process, and the same is true for the corresponding generalized formulas. By comparison with generalized Gaussian summation formulas obtained earlier in a different way, two identities for finite sums involving terminating 3F2(1) series are found. They depend on four or six independent parameters, respectively.

scholarly journals Certain derived WP-bailey pairs and transformation formulas for q-hypergeometric series

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4619-4628 ◽  
Author(s):  
H.M. Srivastava ◽  
S.N. Singh ◽  
S.P. Singh ◽  
Vijay Yadav
Keyword(s):  
Hypergeometric Series ◽  
Bailey Pairs ◽  
Transformation Formulas

In this paper, several results involving the derived WP-Bailey pairs of sequences are established. Furthermore, by using these results, a number of transformation formulas for basic (or q-) hypergeometric series are derived.

Certain applications of WP-Bailey pairs

2019 ◽  
Vol 12 (03) ◽  
pp. 1950049
Author(s):  
Maheshwar Pathak ◽  
Pankaj Srivastava
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Bailey Pairs

In the present paper, certain new transformation formulae for basic hypergeometric series have been developed with the help of new WP-Bailey pair generated from old WP-Bailey pair.

scholarly journals Certain Applications of Generalized Kummer’s Summation Formulas for 2F1

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1538
Author(s):  
Junesang Choi
Keyword(s):  
Hypergeometric Series ◽  
Gamma Functions ◽  
Generalized Hypergeometric Series ◽  
Finite Series ◽  
Summation Formulas

We present generalizations of three classical summation formulas 2F1 due to Kummer, which are able to be derived from six known summation formulas of those types. As certain simple particular cases of the summation formulas provided here, we give a number of interesting formulas for double-finite series involving quotients of Gamma functions. We also consider several other applications of these formulas. Certain symmetries occur often in mathematical formulae and identities, both explicitly and implicitly. As an example, as mentioned in Remark 1, evident symmetries are naturally implicated in the treatment of generalized hypergeometric series.

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