A simple proof of Slater’s transformations for bilateral series ${}_{r}\psi _{r},\, {}_{2r}\psi _{2r}$ and ${}_{2r-1}\psi _{2r-1}$

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2024年1月3日

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Katsuhisa Mimachi

摘要

We give a simple proof of Slater’s transformations for bilateral series ${}_r\psi _r$ $_{r} ψ_{r}$ , ${}_{2r}\psi _{2r}$ $_{2 r} ψ_{2 r}$ , and ${}_{2r-1}\psi _{2r-1}$ $_{2 r - 1} ψ_{2 r - 1}$ , using the residue theorem only, without technical manipulation of the series.

A simple proof of Slater’s transformations for bilateral series \({}_{r}\psi _{r},\, {}_{2r}\psi _{2r}\) and \({}_{2r-1}\psi _{2r-1}\)

摘要