scholarly journals A class of logarithmically completely monotonic functions related to the q-gamma function and applications

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 495-507
Author(s):  
Khaled Mehrez
Keyword(s):  
Gamma Function ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

On the asymptotic expansion of the logarithm of Barnes triple gamma function II

2017 ◽  
Vol 120 (2) ◽  
pp. 291
Author(s):  
Stamatis Koumandos ◽  
Henrik L. Pedersen
Keyword(s):  
Asymptotic Expansion ◽  
Gamma Function ◽  
Positive Order ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

The remainders in an asymptotic expansion of the logarithm of Barnes triple gamma function give rise to completely monotonic functions of positive order.

Completely monotonic functions related to the q-gamma and the q-trigamma functions

2015 ◽  
Vol 13 (02) ◽  
pp. 125-134 ◽  
Author(s):  
Ahmed Salem
Keyword(s):  
Gamma Function ◽  
Infinite Class ◽  
Positive Real ◽  
Digamma Function ◽  
Sharp Bounds ◽  
Monotonic Functions ◽  
Polygamma Function ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

In this paper, two completely monotonic functions involving the q-gamma and the q-trigamma functions where q is a positive real, are introduced and exploited to derive sharp bounds for the q-gamma function in terms of the q-trigamma function. These results, when letting q → 1, are shown to be new. Also, sharp bounds for the q-digamma function in terms of the q-tetragamma function are derived. Furthermore, an infinite class of inequalities for the q-polygamma function is established.

INEQUALITIES ASSOCIATED WITH RATIOS OF GAMMA FUNCTIONS

2018 ◽  
Vol 97 (3) ◽  
pp. 453-458
Author(s):  
JENICA CRINGANU
Keyword(s):  
Gamma Function ◽  
Monotonic Function ◽  
Completely Monotonic Function ◽  
Gamma Functions ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
Appl Math

We use properties of the gamma function to estimate the products$\prod _{k=1}^{n}(4k-3)/4k$and$\prod _{k=1}^{n}(4k-1)/4k$, motivated by the work of Chen and Qi [‘Completely monotonic function associated with the gamma function and proof of Wallis’ inequality’,Tamkang J. Math.36(4) (2005), 303–307] and Morticiet al.[‘Completely monotonic functions and inequalities associated to some ratio of gamma function’,Appl. Math. Comput.240(2014), 168–174].

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