On the Multiple Gamma-Functions
نویسندگان
چکیده
منابع مشابه
THE MULTIPLE GAMMA FUNCTIONS AND THE MULTIPLE q-GAMMA FUNCTIONS
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.
متن کاملThe Multiple Gamma-Functions and the Log-Gamma Integrals
In this paper, which is a companion paper to W , starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log Γ 1± t . This enables us to locate the genesis of two new functions A1/a and C1/a considered by Srivastava and Choi. We consider the closely related function A(a) and the Hurwitz zeta function, which render t...
متن کاملMultiple Gamma and related functions
The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical de nite integral due to Euler and other de nite integrals are also considered together with closed-form evaluations of some series involving the Riemann and Hurwitz Zeta functions.
متن کاملON A q-ANALOGUE OF THE MULTIPLE GAMMA FUNCTIONS
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. 1 2 MICHITOMO NISHIZAWA
متن کاملOn p-adic multiple zeta and log gamma functions
We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1998
ISSN: 0387-3870
DOI: 10.3836/tjm/1270041994