The multiple gamma functions and the multiple q-gamma functions
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We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering the classical limit of the multiple q-gamma functions.
AMS-Latex, 40 pages. Minor changes have been made
AMS-Latex, 40 pages. Minor changes have been made