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

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- by Neal Koblitz PDF
- 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. Moritaโs

*p*-adic gamma function and the derivative of J. Diamondโs

*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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## Additional Information

- © Copyright 1980 American Mathematical Society
- 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