A unified presentation of the Gamma-type functions occurring in diffraction theory and associated probability distributions

• Published in: Applied mathematics and computation 2005-03, Vol.162 (2), p.931-947
• Main Authors: Srivastava, H.M., Saxena, R.K., Ram, Chena
• Format: Article
• Language: English
• Subjects: Diffraction theory; Exact sciences and technology; Functions of a complex variable; Gamma and incomplete Gamma functions; General logic; Generalized hypergeometric function; Hazard (or failure) rate function; Logic and foundations; Mathematical analysis; Mathematical logic, foundations, set theory; Mathematics; Mean residual life (or remaining life expectancy) function; Moment generating function; Numerical analysis; Numerical analysis. Scientific computation; Probability density function; Sciences and techniques of general use; Special functions; Survival (or reliability) function; Wiener–Hopf technique
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2003.12.133

In view of their importance and usefulness in diffraction theory and probability distributions, several generalizations of the Gamma-type functions were investigated extensively in recent years. The main object of this paper is to present a systematic study of a unification and generalization of these Gamma-type functions, which is defined here by means of the Fox–Wright hypergeometric function pΨ q . A probability density function associated with the generalized Gamma-type function investigated in this paper, together with several other related results in the theory of probability and statistics, are also considered.