On the fractional calculus operator involving Gauss´s series and its application to certain statiscal distributions

• Megumi Saigo University Fukuoka-Japón
• R.K. Raina

Abstract

This paper is dealing with a generalized fractional calculus introduced by the first author. The images of some elementary functions under the operators of this calculus are presented in terms of hypergeometric functions. These results are applied to a certain statistical distribution and generalized Dirichlet distributions. Further results concerning these distributions and known particular cases are also mentioned.