Generalized Elliptic Integrals Involving Incomplete Fox Wright Function

Abstract

Elliptic integrals are used in various diverse physical fields (like some exclusive radiation field problems, analysis of crystallographic minimum surface problem, study of electromagnetic waves through an elliptic disk, elliptic crack problems, etc.). Due to these applications a remarkably large number of elliptic integrals are defined and studied earlier. Motivated by these works we have derived some new elliptic integrals involving an incomplete Fox-Wright function. The results established in this paper are basic in nature and can be reduced in many special cases. Some of the special cases are mentioned here as corollaries.