Characterization of the Euler gamma function with the aid of an arbitrary mean

2018 ◽  
Vol 93 (1-2) ◽  
pp. 163-170
Author(s):  
Janusz Matkowski
Keyword(s):  
Gamma Function ◽  
Euler Gamma Function

A Simple Characterization of the Gamma Function

1987 ◽  
Vol 94 (6) ◽  
pp. 534-536 ◽  
Author(s):  
Detlef Laugwitz ◽  
Bernd Rodewald
Keyword(s):  
Gamma Function ◽  
Simple Characterization

scholarly journals Quantum Barnes Function as the Partition Function of the Resolved Conifold

2008 ◽  
Vol 2008 ◽  
pp. 1-47
Author(s):  
Sergiy Koshkin
Keyword(s):  
Partition Function ◽  
Holomorphic Function ◽  
Gamma Function ◽  
Euler Gamma Function ◽  
New Formula ◽  
Chern Simons

We give a short new proof of largeNduality between the Chern-Simons invariants of the 3-sphere and the Gromov-Witten/Donaldson-Thomas invariants of the resolved conifold. Our strategy applies to more general situations, and it is to interpret the Gromov-Witten, the Donaldson-Thomas, and the Chern-Simons invariants as different characterizations of the same holomorphic function. For the resolved conifold, this function turns out to be the quantum Barnes function, a naturalq-deformation of the classical one that in its turn generalizes the Euler gamma function. Our reasoning is based on a new formula for this function that expresses it as a graded product ofq-shifted multifactorials.

A Simple Characterization of the Gamma Function

1987 ◽  
Vol 94 (6) ◽  
pp. 534 ◽  
Author(s):  
Detlef Laugwitz ◽  
Bernd Rodewald
Keyword(s):  
Gamma Function ◽  
Simple Characterization

scholarly journals A note on an inequality for the gamma function

1978 ◽  
Vol 1 (2) ◽  
pp. 227-233 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Gamma Function ◽  
Convex Functions

Some inequalities for the Wallis functions are proved. The results of this paper are consequences of some characterization of convex functions. A generalization of a result of Boyd (1) and an extentlon of an inequality of Gantschi (3) are obtained.

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