Abstract
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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Acknowledgements
The author would like to thank Ryojun Ito, Hiroyuki Ochiai, Nobuki Takayama and Raimundas Vidūnas for helpful discussions, and the referee for bibliographical remarks.
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This work is supported by JSPS Grant-in-Aid for Scientific Research: 18K03234.
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Otsubo, N. A new approach to hypergeometric transformation formulas. Ramanujan J 55, 793–816 (2021). https://doi.org/10.1007/s11139-020-00286-7
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DOI: https://doi.org/10.1007/s11139-020-00286-7