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.

scholarly journals On the asymptotic expansion of the logarithm of Barnes triple gamma function

2009 ◽  
Vol 105 (2) ◽  
pp. 287 ◽  
Author(s):  
Stamatis Koumandos ◽  
Henrik L. Pedersen
Keyword(s):  
Asymptotic Expansion ◽  
Gamma Function ◽  
Error Bounds ◽  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions

It is shown that the remainders in an asymptotic expansion of the logarithm of Barnes triple gamma function give rise to completely monotonic functions. Furthermore, error bounds are found.

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.

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