A new approach to hypergeometric transformation formulas

We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi’s canonical form of the hypergeometric differential equation. Analogy for q -hypergeometric functions is also studied.

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Bibliographic Details
Published in:The Ramanujan journal Vol. 55; no. 2; pp. 793 - 816
Main Author: Otsubo, Noriyuki
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2021
Springer Nature B.V
Subjects:
Canonical forms
Combinatorics
Differential equations
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Hypergeometric functions
Mathematics
Mathematics and Statistics
Number Theory
Transformations (mathematics)
Hypergeometric functions
Basic hypergeometric functions
Transformation formulas
33C05
33D15
ISSN:1382-4090, 1572-9303
Online Access:Get full text
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Description
Summary:We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi’s canonical form of the hypergeometric differential equation. Analogy for q -hypergeometric functions is also studied.
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00286-7