Searcharxiv⌕ Search

arXiv subjects

Arjun K. Rathie

Publications and source records attributed to Arjun K. Rathie.

23 records · Page 2Linked to original sources
arXiv2013

Remark On Two Results due to Ramanujan on Hypergeometric Series

During the course of verifying the results of Ramanujan on hypergeometric series, Berndt in his notebooks, Part II mentioned corrected forms of two of the Ramanujan's results. The aim of this short research note is to point out that one of the results obtained by Ramanujan is correct (and not of Berndt's result) and the second result (which is slightly differ from Ramanujan's result and Berndt's result) is given here in corrected form.

math.CV↗
arXiv2013

On the Distribution of the Product and the Sum of Generalized Shifted Gamma Random Variables

In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of ordinary Meijer G and H functions. This way, the need of defining new functions which easily enable one to write such integrals in a closed-form is inherent to the development of this area of statistical sciences. By generalizing the Mellin transform which defines the H function, a new function is established. A direct application of the so-called $\widehat{I}$ is discussed while developing the probability density function of the sum and the product of shifted generalized gamma random variables. Important special cases of the $\widehat{I}$ and their applications in science are also discussed in order to show the applicability of the function hereby defined.

math.CV↗
arXiv2012

A study of I-functions of two variables

In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series representation, behavior for small values, elementary properties and some special cases for the I-functions of two variables are also discussed.

math.CV↗
arXiv2012

A new generalization of generalized hypergeometric functions

In this paper a natural generalization of the familiar H -function of Fox namely the I -function is proposed. Convergence conditions, various series representations, elementary properties and special cases for the I -function have also been given.

math.CV↗