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1. Some best approximation formulas and inequalities for the Bateman's G-function.

Author

Hegazi, Ahmed, Mahmoud, Mansour, Talat, Ahmed, and Moustafa, Hesham

Subjects
*APPROXIMATION theory, *FUNCTIONAL analysis, *MATHEMATICAL functions, *MATHEMATICAL constants, *MATHEMATICS
Abstract

In the paper, the authors established two best approximation formulas for the Bateman's G-function. Also, they studied the completely monotonicity of some functions involving G(x). Some new inequalities are deduced for the function and its derivative such as 1/2 ln [1 + 2x + a/x2 + 2x + 4/3 ] < G(x + 2) < 1/2 ln [ 1 + 2x + b/x2 + 2x + 4/3 ], x > 0 where a = 3 and b = e4-16/12 are the best possible constants. Our results improve some recent inequalities about the function G(x). [ABSTRACT FROM AUTHOR]

Published
2019

2. Some new inequalities for the gamma function.

Author

Xiaodong Cao

Subjects
*BETA distribution, *GAMMA functions, *DERIVATIVES (Mathematics), *MATHEMATICS, *MATHEMATICAL functions
Abstract

In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in [6, 7] and a generalized Mortici's lemma. [ABSTRACT FROM AUTHOR]

Published
2016