𝑞-extension of the 𝑝-adic gamma function

Koblitz, Neal

doi:10.1090/S0002-9947-1980-0574791-5

$q$-extension of the $p$-adic gamma function
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Trans. Amer. Math. Soc. 260 (1980), 449-457 Request permission

Abstract:

p-adic functions depending on a parameter q, $0 < |q - 1{|_p} < 1$, are defined which extend Y. Morita’s p-adic gamma function and the derivative of J. Diamond’s p-adic log-gamma function in the same way as the classical q-gamma function ${\Gamma _q}(x)$ extends $\Gamma (x)$. Properties of these functions which are analogous to the basic identities satisfied by ${\Gamma _q}(x)$ are developed.

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41

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