Integral representation of some functions related to the Gamma function
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
Authors:
Christian Berg
Abstract
We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.
Cite
@article{arxiv.math/0411550,
title = {Integral representation of some functions related to the Gamma function},
author = {Christian Berg},
journal= {arXiv preprint arXiv:math/0411550},
year = {2007}
}
Related papers
View all related →
Mathematical Physics · Physics
Integral and series representations of the digamma and polygamma functions
Mark W. Coffey
2010-08-25
Classical Analysis and ODEs · Mathematics
Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action
Omran Kouba
2017-02-20
Classical Analysis and ODEs · Mathematics
Some applications of the Stieltjes constants
Donal F. Connon
2009-01-15
Classical Analysis and ODEs · Mathematics
Some logarithmically completely monotonic functions related to the gamma function
Feng Qi, Bai-Ni Guo
2010-08-03
Classical Analysis and ODEs · Mathematics
A Pick function related to the sequence of volumes of the unit ball in n-space
Christian Berg, Henrik L. Pedersen
2009-12-14
General Mathematics · Mathematics
Integrals Associated with the Digamma Integral Representation
Richard J. Mathar
2023-08-29
General Mathematics · Mathematics
Two integral representations for the logarithm of the Glaisher-Kinkelin constant
Jean-Christophe Pain
2024-05-10
Classical Analysis and ODEs · Mathematics
Ratios of Entire functions and generalized Stieltjes functions
Dimitris Askitis, Henrik L. Pedersen
2021-07-05
Classical Analysis and ODEs · Mathematics
Nielsen's beta function and some infinitely divisible distributions
Christian Berg, Stamatis Koumandos, Henrik L. Pedersen
2019-09-23
Number Theory · Mathematics
A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations
Iaroslav V. Blagouchine
2015-07-08
Complex Variables · Mathematics
Functional equations for the Stieltjes constants
Mark W. Coffey
2014-05-20
Mathematical Physics · Physics
Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders
Christian D. Tica, Eric A. Galapon
2019-04-24
Complex Variables · Mathematics
Stieltjes, Poisson and other integral representations for functions of Lambert $W$
German A. Kalugin, David J. Jeffrey, Robert M. Corless
2011-03-30
Number Theory · Mathematics
A curious formula related to the Euler Gamma function
Bakir Farhi
2013-12-30
Classical Analysis and ODEs · Mathematics
Integral representations and properties of some functions involving the logarithmic function
Feng Qi, Wen-Hui Li
2016-08-22
Number Theory · Mathematics
On gamma functions with respect to the alternating Hurwitz zeta functions
Wanyi Wang, Su Hu, Min-Soo Kim
2025-04-28
Classical Analysis and ODEs · Mathematics
On generalized Stieltjes functions
Stamatis Koumandos, Henrik L. Pedersen
2017-06-05
Classical Analysis and ODEs · Mathematics
Stieltjes functions of finite order and hyperbolic monotonicity
Lennart Bondesson, Thomas Simon
2016-04-19
Classical Analysis and ODEs · Mathematics
Pick Functions Related to the Multiple Gamma Functions of order $n$
Sourav Das, A. Swaminathan
2016-01-14
Mathematical Physics · Physics
Series representations for the Stieltjes constants
Mark W. Coffey
2009-09-14
Combinatorics · Mathematics
On a series for the upper incomplete Gamma function
Mario DeFranco
2019-09-17
General Mathematics · Mathematics
Representations of the Glaisher-Kinkelin constant deduced from integrals due to F\'eaux and Kummer
Jean-Christophe Pain
2024-10-31
Classical Analysis and ODEs · Mathematics
Normed modules and The Stieltjes integrations of functions defined on finite-dimensional algebras
Hanpeng Gao, Shengda Liu, Yu-Zhe Liu, Yucheng Wang
2024-06-04
Mathematical Physics · Physics
Series representations of the Riemann and Hurwitz zeta functions and series and integral representations of the first Stieltjes constant
Mark W. Coffey
2011-06-28
Mathematical Physics · Physics
On representations and differences of Stieltjes coefficients, and other relations
Mark W. Coffey
2008-12-09