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Abstract. A q-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.1995 Mathematical Subject Classification. 33D05, 81R50

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass canonical product representation) of the Vigneras multiple gamma functions by considering the classical limit of the multiple #-gamma functions.

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