Multiple Gamma Functions and Multiple -Gamma Functions

  • Kimio Ueno

    Waseda University, Tokyo, Japan
  • Michitomo Nishizawa

    Waseda University, Tokyo, Japan


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.

Cite this article

Kimio Ueno, Michitomo Nishizawa, Multiple Gamma Functions and Multiple -Gamma Functions. Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, pp. 813–838

DOI 10.2977/PRIMS/1195145019