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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0574791-5
MathSciNet review: 574791
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Abstract: p-adic functions depending on a parameter q, $0 < |q - 1{|_p} < 1$, are defined which extend Y. Moritaโ€™s p-adic gamma function and the derivative of J. Diamondโ€™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, <I>p</I>-adic functions, <I>q</I>-extension, Euler constants
Article copyright: © Copyright 1980 American Mathematical Society