Some transformation formulas of $q$-hypergeometric series via contour integration

2020 ◽  
pp. 1
Author(s):  
Kam Cheong Au
Keyword(s):  
Hypergeometric Series ◽  
Contour Integration ◽  
Transformation Formulas

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.

Values of Gaussian hypergeometric series and their connections to algebraic curves

2017 ◽  
Vol 14 (01) ◽  
pp. 1-18 ◽  
Author(s):  
Gautam Kalita
Keyword(s):  
Hypergeometric Series ◽  
Algebraic Curves ◽  
Vital Role ◽  
Special Values ◽  
Transformation Formulas ◽  
Gaussian Hypergeometric Series

In this paper, we explicitly evaluate certain special values of [Formula: see text] hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of the number of points on certain algebraic curves over [Formula: see text] in terms of Gaussian hypergeometric series, which play the vital role in deducing the transformation results.

scholarly journals Certain transformations for hypergeometric series in the p-adic setting

2015 ◽  
Vol 11 (02) ◽  
pp. 645-660 ◽  
Author(s):  
Rupam Barman ◽  
Neelam Saikia
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Gamma Function ◽  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Transformation Formulas ◽  
Trace Of Frobenius

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236], McCarthy defined a function nGn[⋯] using the Teichmüller character of finite fields and quotients of the p-adic gamma function. This function extends hypergeometric functions over finite fields to the p-adic setting. In this paper, we give certain transformation formulas for the function nGn[⋯] which are not implied from the analogous hypergeometric functions over finite fields.

Sign in / Sign up

Export Citation Format

Share Document