scholarly journals Refinements of Some Recent Inequalities for Certain Special Functions

2019 ◽  
Vol 33 (1) ◽  
pp. 1-20
Author(s):  
Mohamed Akkouchi ◽  
Mohamed Amine Ighachane
Keyword(s):  
Gamma Function ◽  
Generalized Inverse ◽  
Special Functions ◽  
Integral Function ◽  
Inverse Gaussian ◽  
Exponential Integral ◽  
Generalized Inverse Gaussian Distribution ◽  
Normalizing Constant ◽  
Lerch Zeta Function ◽  
Generalized Inverse Gaussian

AbstractThe aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no. 2, 124–129] for the incomplete gamma function, Polygamma functions, Exponential integral function, Abramowitz function, Hurwitz-Lerch zeta function and for the normalizing constant of the generalized inverse Gaussian distribution and the Remainder of the Binet’s first formula for ln Γ(x).

scholarly journals On an extension of generalized incomplete Gamma functions with applications

1996 ◽  
Vol 37 (3) ◽  
pp. 392-405 ◽  
Author(s):  
M. Aslam Chaudhry ◽  
S. M. Zubair
Keyword(s):  
Gaussian Distribution ◽  
Generalized Inverse ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Generalized Inverse Gaussian Distribution ◽  
Gamma Functions ◽  
Generalized Gamma ◽  
Incomplete Gamma Functions ◽  
Generalized Inverse Gaussian ◽  
Class Of Functions

AbstractIn this paper we have introduced extensions νυ(α, x; b) and Γν(α, x; b) of the generalized Gamma functions γ(α x; b) and Γ(α, x; b) considered recently by Chaudhry and Zubair. These extensions are found useful in the representations of the Laplace and K-transforms of a class of functions. We have also defined a generalization of the inverse Gaussian distribution. The cumulative and the reliability functions of the generalized inverse Gaussian distribution are expressed in terms of these functions. Some useful properties of the functions are also discussed.

Sign in / Sign up

Export Citation Format

Share Document