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$q$-extension of the $p$-adic gamma function
1980
Transactions of the American Mathematical Society
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p-adic functions depending on a parameter q, 0 < \q -l\p < 1, are defined which extend Y. Morita's p-adic gamma function and the derivative of J. Diamond's /»-adic log-gamma function in the same way as the classical ç-gamma function Tq(x) extends T(x). Properties of these functions which are analogous to the basic identities satisfied by Tq(x) are developed.
doi:10.1090/s0002-9947-1980-0574791-5
fatcat:yyeahk4gxjb5ljzsl4m52pt5sy