Raabe’s formula for $p$-adic gamma and zeta functions

@article{Cohen2008,
abstract = {The classical Raabe formula computes a definite integral of the logarithm of Euler’s $\Gamma $-function. We compute $p$-adic integrals of the $p$-adic $\log \Gamma $-functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and $p$-adic Raabe formula. We also prove a Raabe-type formula for $p$-adic Hurwitz zeta functions.},
affiliation = {Université Bordeaux I Institut de Mathématiques U.M.R. 5251 du C.N.R.S. 351 Cours de la Libération, 33405 Talence Cedex (France); Universidad de Chile Facultad de Ciencias Departamento de Matemática Casilla 653 Santiago (Chile)},
author = {Cohen, Henri, Friedman, Eduardo},
journal = {Annales de l’institut Fourier},
keywords = {$p$-adic gamma function; $p$-adic zeta function; Raabe’s formula; -adic gamma function; -adic zeta function; Raabe's formula},
language = {eng},
number = {1},
pages = {363-376},
publisher = {Association des Annales de l’institut Fourier},
title = {Raabe’s formula for $p$-adic gamma and zeta functions},
url = {http://eudml.org/doc/10315},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Cohen, Henri
AU - Friedman, Eduardo
TI - Raabe’s formula for $p$-adic gamma and zeta functions
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 1
SP - 363
EP - 376
AB - The classical Raabe formula computes a definite integral of the logarithm of Euler’s $\Gamma $-function. We compute $p$-adic integrals of the $p$-adic $\log \Gamma $-functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and $p$-adic Raabe formula. We also prove a Raabe-type formula for $p$-adic Hurwitz zeta functions.
LA - eng
KW - $p$-adic gamma function; $p$-adic zeta function; Raabe’s formula; -adic gamma function; -adic zeta function; Raabe's formula
UR - http://eudml.org/doc/10315
ER -