Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ q$-extension of the $ p$-adic gamma function

Author: Neal Koblitz
Journal: Trans. Amer. Math. Soc. 260 (1980), 449-457
MSC: Primary 12B40; Secondary 33A15
MathSciNet review: 574791
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Abstract: p-adic functions depending on a parameter q, $ 0\, < \,\vert q\, - \,1{\vert _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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Keywords: Gamma function, p-adic functions, q-extension, Euler constants
Article copyright: © Copyright 1980 American Mathematical Society