Abstract
Motivated essentially by their importance and usefulness in diffraction theory and probability distributions, several interesting generalizations of the Gamma-type functions were investigated extensively in recent years. In this sequel, to these earlier investigations on the subject, the authors present a systematic study of a unification and generalization of some of these Gamma-type functions, which is defined here by means of certain close relatives of the Fox–Wright hypergeometric function
p
Ψ
q
(z), including e.g., the generalized Lommel–Wright function . A probability density function associated with the generalized Gamma-type function investigated in this article, together with several other related results in the theory of probability and statistics, are also considered.
Keywords:
- Generalized Lommel–Wright function
- Gamma and incomplete Gamma functions
- Fox–Wright hypergeometric function
- Tricomi function
- Srivastava–Daoust multivariable hypergeometric function
- Diffraction theory
- Wiener–Hopf technique
- Probability density function
- Moment generating function
- Survival (or reliability) function
- Hazard (or failure) rate function
- Mean residual life (or remaining life expectancy) function
Acknowledgements
The present investigation was supported, in part, by CONDES (Consejo de Desarrolo Cientifico y Humanístico) de la Universidad del Zulia and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.