scholarly journals Logarithmic derivative of the Euler $\Gamma$-function in Clifford analysis

2005 ◽  
pp. 695-728
Author(s):  
Guy Laville ◽  
Louis Randriamihamison
Keyword(s):  
Gamma Function ◽  
Clifford Analysis ◽  
Logarithmic Derivative ◽  
Euler Gamma Function

scholarly journals On a Conjecture of Alzer, Berg, and Koumandos

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1031
Author(s):  
Ladislav Matejíčka
Keyword(s):  
Gamma Function ◽  
Open Problem ◽  
Logarithmic Derivative ◽  
Completely Monotonic

In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ ( x ) denotes the logarithmic derivative of Euler’s gamma function.

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.

scholarly journals On Some Complete Monotonicity of Functions Related to Generalized k − Gamma Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hesham Moustafa ◽  
Hanan Almuashi ◽  
Mansour Mahmoud
Keyword(s):  
Lower Bounds ◽  
Gamma Function ◽  
Logarithmic Derivative ◽  
Complete Monotonicity ◽  
Upper And Lower Bounds ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

In this paper, we presented two completely monotonic functions involving the generalized k − gamma function Γ k x and its logarithmic derivative ψ k x , and established some upper and lower bounds for Γ k x in terms of ψ k x .

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