Results 11 to 20 of about 685,794 (281)
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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The multiple gamma function and its q-analogue [PDF]
Banach Center Publications, 1996 We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vign\'{e}ras multiple gamma function by considering the classical limit of the multiple q-gamma function.Comment:
Nishizawa, Michitomo, Ueno, Kimio
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Jackson's integral of multiple Hurwitz–Lerch zeta functions and multiple gamma functions [PDF]
Journal of Mathematical Analysis and Applications, 2018 Using the Jackson integral, we obtain the $q$-integral analogue of the Raabe type formulas for Barnes multiple Hurwitz-Lerch zeta functions and Barnes and Vardi's multiple gamma functions. Our results generalize $q$-integral analogue of the Raabe type formulas for the Hurwitz zeta functions and log gamma functions in [N. Kurokawa, K.
Su Hu, Daeyeoul Kim, Min-Soo Kim
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Special values of multiple gamma functions [PDF]
Journal de théorie des nombres de Bordeaux, 2008 We give a Chowla-Selberg type formula that connects a generalization of the eta-function to GL(n) with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Duke, William, Imamoḡlu, Özlem
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Multiple Gamma functions and $L$-functions [PDF]
Mathematical Research Letters, 1996 Multiple gamma functions, first introduced and studied by E. W. Barnes and others around 1900, play an important role in the study of functional equations for Selberg zeta functions and other topics in modern analytic number theory. This paper makes a case for defining a multiple gamma function as a meromorphic function \(\Gamma_P(u)\) associated with ...
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Multiple $$\log \Gamma $$ -Type Functions
, 2022 AbstractIn this chapter, we introduce and investigate the map, denote it by Σ, that carries any function g lying in $$\displaystyle \bigcup _{p\geq 0}(\mathcal {D}^p\cap \mathcal {K}^p) $$ ⋃ p ≥ 0
Jean-Luc Marichal, Naïm Zenaïdi
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Bounds for triple gamma functions and their ratios
Journal of Inequalities and Applications, 2016 In this work, in addition to the bounds for triple gamma function, bounds for the ratios of triple gamma functions are obtained. Similar bounds for the ratios of the double gamma functions are also obtained.
Sourav Das, A Swaminathan
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Theory of Barnes Beta Distributions [PDF]
, 2013 A new family of probability distributions $\beta_{M, N},$ $M=0\cdots N,$ $N\in\mathbb{N}$ on the unit interval $(0, 1]$ is defined by the Mellin transform.
Ostrovsky, Dmitry
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