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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Vydáno v:The Ramanujan journal Ročník 55; číslo 2; s. 793 - 816
Hlavní autor: Otsubo, Noriyuki
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2021
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00286-7