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A generalisation of an expansion for the Riemann zeta function involving incomplete gamma functions
Zeta function Incomplete gamma functions
2010/9/17
We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive intege...
A NOTE ON LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA FUNCTIONS
completely monotonic function logarithmically completely monotonic function gamma function
2008/11/25
The function (x=e)x
G(x+1=2) strictly logarithmically completely monotonic on (0;¥) is
proved and an alternative proof of the function [G(x+1)]1=x
x ¡1+ 1x
¢x strictly logarithmical...
Monotonicity of Ratios Involving Incomplete Gamma Functions with Actuarial Applications
Gamma function Monotonicity Weighted distributions Tail expectations
2010/1/22
Ratios involving incomplete gamma functions and their monotonicity properties play important roles in financial risk analysis. We derive desired monotonicity properties either using Pinelis' Calculus ...
On the $q$-Analogue of Gamma Functions and Related Inequalities
Euler gamma function $q$-gamma function
2008/6/27
In this paper, we obtain a q-analogue of a double inequality involving the Euler gamma function which was first proved geometrically by Alsina and Tomás [1] and then analytically by Sándor [6].