On Generating Relations and Identities for I-Function
by
Rajendra Singh Enaniya
Teacher Fellow,Dept.of Mathematics and Statistics,JNU University,Rajasthan,India.
Coauthors: Chena Ram, Department of Mathematics and Statistics Jai Narain Vyas University, Jodhpur-342005(Raj.), INDIA

In the present paper, certain generating relations and identities for I-Function, which is the generalization of the Hyper-geometric functions and the Fox’s H-function, have been obtained. The Importance of this function is due to the fact there the property of H-function permits it to adopt the analytic continuation of any complex plane, where the poles and the empty products are defined on the extended complex plane, whereas the integral representation of this function is given in terms of Mellin-Barnes contour integration. The singularities of the Gamma-Functions and appropriate manipulation of the finite products reasonably help this function to produce various summation transformations.

The Present paper involves, in evaluating the generating relations and identities, some known results in terms of Kummer’s Hyper-Geometric functions, Gauss-Hyper-geometric functions and owing to their employments and by adjustment of parameters for the I-Function, in question, we could obtain 15 Generating Relations and by the application of change of order of integration and summation, 9 identities, relating to this function have been obtained.

R.S.Enaniya (Teacher Fellow)

Department of Mathematics and Statistics

Jai Narain Vyas University, Jodhpur-342005(Raj.), INDIA

Email: r.enaniya@gmail.com

Date received: January 22, 2008