We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the classical limit of the multiple q-gamma function.
@article{bwmeta1.element.bwnjournal-article-bcpv40z1p429bwm,
author = {Ueno, Kimio and Nishizawa, Michitomo},
title = {The multiple gamma function and its q-analogue},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {429-441},
zbl = {0869.33001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p429bwm}
}
Ueno, Kimio; Nishizawa, Michitomo. The multiple gamma function and its q-analogue. Banach Center Publications, Tome 38 (1997) pp. 429-441. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p429bwm/
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