A transformation formula for multiple hypergeometric series

1967 ◽  
Vol 71 (1) ◽  
pp. 1-6 ◽  
Author(s):  
L. Carlitz
Keyword(s):  
Hypergeometric Series ◽  
Transformation Formula ◽  
Multiple Hypergeometric Series

scholarly journals The sum of a multiple hypergeometric series

1977 ◽  
Vol 80 (5) ◽  
pp. 448-452 ◽  
Author(s):  
H.M Srivastava
Keyword(s):  
Hypergeometric Series ◽  
Multiple Hypergeometric Series

scholarly journals Some q-generating functions associated with basic multiple hypergeometric series

1994 ◽  
Vol 27 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Th.M. Rassias ◽  
S.N. Singh ◽  
H.M. Srivastava
Keyword(s):  
Generating Functions ◽  
Hypergeometric Series ◽  
Multiple Hypergeometric Series

scholarly journals A note on the convergence of certain families of multiple hypergeometric series

1992 ◽  
Vol 164 (1) ◽  
pp. 104-115 ◽  
Author(s):  
NguyêñThanh Hái ◽  
O.I Marichev ◽  
H.M Srivastava
Keyword(s):  
Hypergeometric Series ◽  
Multiple Hypergeometric Series

scholarly journals Massive one-loop conformal Feynman integrals and quadratic transformations of multiple hypergeometric series

2021 ◽  
Vol 103 (9) ◽  
Author(s):  
B. Ananthanarayan ◽  
Sumit Banik ◽  
Samuel Friot ◽  
Shayan Ghosh
Keyword(s):  
Hypergeometric Series ◽  
Feynman Integrals ◽  
Multiple Hypergeometric Series

scholarly journals A transformation formula for double hypergeometric series

1973 ◽  
Vol 3 (3) ◽  
pp. 377-382 ◽  
Author(s):  
R.P. Singal
Keyword(s):  
Hypergeometric Series ◽  
Transformation Formula

scholarly journals Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

2020 ◽  
Author(s):  
Victor J. W. Guo ◽  
Michael J. Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Double Series ◽  
Summation Formula ◽  
Transformation Formula ◽  
Quadratic Transformation ◽  
Ultraspherical Polynomials ◽  
Higher Power ◽  
Series Transformation ◽  
Transformation Formulas

AbstractSeveral new q-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in collaboration with Zudilin. More concretely, the results in this paper include q-analogues of supercongruences (referring to p-adic identities remaining valid for some higher power of p) established by Long, by Long and Ramakrishna, and several other q-supercongruences. The six basic hypergeometric transformation formulas which are made use of are Watson’s transformation, a quadratic transformation of Rahman, a cubic transformation of Gasper and Rahman, a quartic transformation of Gasper and Rahman, a double series transformation of Ismail, Rahman and Suslov, and a new transformation formula for a nonterminating very-well-poised $${}_{12}\phi _{11}$$ 12 ϕ 11 series. Also, the nonterminating q-Dixon summation formula is used. A special case of the new $${}_{12}\phi _{11}$$ 12 ϕ 11 transformation formula is further utilized to obtain a generalization of Rogers’ linearization formula for the continuous q-ultraspherical polynomials.

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