Corrigendum to “Some complete monotonicity properties for the (p,q)-gamma function”

SOME MONOTONICITY PROPERTIES OF GAMMA AND q-GAMMA FUNCTIONS

We prove some properties of completely monotonic functions and apply them to obtain results on gamma and q-gamma functions.

Complete monotonicity involving some ratios of gamma functions

In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi's and Ismail's conclusions, but also can generate some new inequali...

Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function

In the paper, the authors establish integral representations of some functions related to the remainder of Burnside’s formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These results extend and generalize some known conclusions. 1. Motivation and main results A function f is said to be completely monotonic on an interval I if f ha...

Monotonicity and Convexity for the Gamma Function

Let a and b be given real numbers with 0 ≤ a < b < a + 1. Then the function θa,b(x) = [Γ(x + b)/Γ(x + a)]1/(b−a) − x is strictly convex and decreasing on (−a,∞) with θa,b(∞) = a+b−1 2 and θa,b(−a) = a, where Γ denotes the Euler’s gamma function.

Monotonicity and inequalities for the gamma function