scholarly journals A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder

2020 ◽  
Vol 148 (5) ◽  
pp. 2163-2178 ◽  
Author(s):  
Zhen-Hang Yang ◽  
Jing-Feng Tian ◽  
Ming-Hu Ha
Keyword(s):  
Asymptotic Expansion ◽  
Complete Monotonicity ◽  
Gamma Functions

scholarly journals On the complete monotonicity of quotient of gamma functions

2012 ◽  
pp. 395-402 ◽  
Author(s):  
Yi-Chao Chen ◽  
Toufik Mansour ◽  
Qian Zou
Keyword(s):  
Complete Monotonicity ◽  
Gamma Functions

scholarly journals COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

2013 ◽  
Vol 88 (2) ◽  
pp. 309-319 ◽  
Author(s):  
FENG QI ◽  
PIETRO CERONE ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Divided Difference ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complete Monotonicity ◽  
Divided Differences ◽  
Psi Function ◽  
Gamma Functions ◽  
Completely Monotonic ◽  
Polygamma Functions ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

scholarly journals A Solution to Qi’s Conjecture on a Double Inequality for a Function Involving the Tri- and Tetra-Gamma Functions

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1098 ◽  
Author(s):  
Ladislav Matejíčka
Keyword(s):  
Open Problem ◽  
Complete Monotonicity ◽  
Double Inequality ◽  
Gamma Functions

In the paper, the author gives a solution to a conjecture on a double inequality for a function involving the tri- and tetra-gamma functions, which was first posed in Remark 6 of the paper “Complete monotonicity of a function involving the tri- and tetragamma functions” (2015) and repeated in the seventh open problem of the paper “On complete monotonicity for several classes of functions related to ratios of gamma functions” (2019).

scholarly journals An asymptotic expansion for a ratio of products of gamma functions

2000 ◽  
Vol 24 (8) ◽  
pp. 505-510 ◽  
Author(s):  
Wolfgang Bühring
Keyword(s):  
Asymptotic Expansion ◽  
Gamma Functions

An asymptotic expansion of a ratio of products of gamma functions is derived. It generalizes a formula which was stated by Dingle, first proved by Paris, and recently reconsidered by Olver

Corrigendum and addendum to ‘asymptotic series for double zeta, double gamma and Hecke L-functions’

2002 ◽  
Vol 132 (2) ◽  
pp. 377-384 ◽  
Author(s):  
KOHJI MATSUMOTO
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Series ◽  
Gamma Functions ◽  
Double Zeta ◽  
Error Terms

Refined expressions are given for the error terms in the asymptotic expansion formulas for double zeta and double gamma functions, proved in the author's former paper [2]. Some inaccurate claims in [2] are corrected.

An integral representation of the Catalan numbers

2015 ◽  
Vol 3 (3) ◽  
pp. 130 ◽  
Author(s):  
Xiao-Ting Shi ◽  
Fang-Fang Liu ◽  
Feng Qi
Keyword(s):  
Integral Representation ◽  
Open Problem ◽  
Catalan Numbers ◽  
Complete Monotonicity ◽  
Gamma Functions

<p><span>In the paper, the authors establish an integral representation of the Catalan numbers, connect the Catalan numbers with the (logarithmically) complete monotonicity, and pose an open problem on the logarithmically complete monotonicity of a function involving ratio of gamma functions.</span></p>

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