Results 11 to 20 of about 682,858 (276)
The multiple gamma functions and the multiple q-gamma functions
Publications of the Research Institute for Mathematical Sciences, 1996 We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vign\'{e}ras multiple gamma functions by considering the classical limit of the multiple q-gamma ...
Nishizawa, Michitomo, Ueno, Kimio
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The Multiple Gamma-Functions and the Log-Gamma Integrals [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 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 .
X.-H. Wang, Y.-L. Lu
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On a q-analogue of the multiple gamma functions [PDF]
Letters in Mathematical Physics, 1995 A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem.
A. Voros +16 more
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A complete monotonicity property of the multiple gamma function [PDF]
Comptes Rendus. Mathématique, 2020 We consider the following functions \[ f_n(x)=1-\ln x+\frac{\ln G_n(x+1)}{x} \text{ and }g_n(x)=\frac{\@root x \of {G_n(x+1)}}{x},\; x\in (0,\infty ),\; n\in \mathbb{N}, \] where $G_n(z)=\left(\Gamma _n(z)\right)^{(-1)^{n-1}}$ and $\Gamma _n$ is the ...
Das, Sourav
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On Barnes' Multiple Zeta and Gamma Functions
Advances in Mathematics, 2000 In this paper the author presents new frameworks for studying Barnes' multiple zeta and gamma functions. Barnes' multiple zeta function defined as \[ \zeta_{N}(s, w |a_{1}, \ldots, a_{N}) \quad = \sum_{m_{1}, \ldots, m_{N} = 0}^{\infty} (w+m_{1}a_{1}+ \cdots + m_{N}a_{N})^{-s}, \] \[ \operatorname {Re} w > 0, \;\operatorname {Re} s > N,\;a_{i}>0 \quad (
Simon Nm Ruijsenaars
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On p-adic multiple zeta and log gamma functions
Journal of Number Theory, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tangedal, Brett A., Young, Paul T.
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Rational series for multiple zeta and log gamma functions
Journal of Number Theory, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On criteria for algebraic independence of collections of functions satisfying algebraic difference relations [PDF]
Opuscula Mathematica, 2017 This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras ...
Hiroshi Ogawara
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Frontiers in Systems Neuroscience, 2021 This article describes a neural model of the anatomy, neurophysiology, and functions of intrinsic and extrinsic theta rhythms in the brains of multiple species.
Stephen Grossberg
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Inequalities Involving $q$-Analogue of Multiple Psi Functions
Comptes Rendus. Mathématique, 2020 Logarithmic derivative of the multiple gamma function is known as the multiple psi function. In this work $q$-analogue of multiple psi functions of order $n$ have been considered.
Das, Sourav
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