Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions. (21st June 2016)

• Record Type: Journal Article
• Authors: Srivastava, H. M.; Agarwal, Ritu; Jain, Sonal
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 1(2017)
• Page Start: 255
• Page End: 273
• Publication Date: 2016-06-21
• Subjects: extended generalized hypergeometric functions -- generalized beta function -- fox‐wright generalized hypergeometric function -- integral transforms -- hypergeometric fractional derivatives -- Riemann–Liouville, Weyl, Erdélyi–Kober and other fractional derivative operators -- probability distributions -- probability generating functions -- Ramanujan's master theorem -- probability density functions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3986
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In the present paper, our aim is to establish several formulas involving integral transforms, fractional derivatives, and a certain family of extended generalized hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results. A probability density function involving the extended generalized hypergeometric function is introduced, and its properties are studied. The corresponding properties of some of the classical probability distributions and their associated probability density functions are easily derivable as special cases of our general results. Copyright © 2016 John Wiley & Sons, Ltd.