FINITE INTEGRALS INVOLVING INCOMPLETE ALEPH FUNCTIONS, EXTENSION OF THE MITTAG-LEFFLER FUNCTION AND ELLIPTIC INTEGRAL OF FIRST SPECIES

Document Type : Regular research papers

Abstract

In recent years, many authors have explored wide variety of in-
tegrals involving special functions. To continue the study, in the present pa-
per, we evaluate the general finite integral involving the elliptic integral of
first species, extension of the Mittag-Leffler function and the incomplete Aleph-
functions by application of known integral given by Brychkov. At the end, in
consequence of general character of functions involved in this study, we shall
see new results as several corollaries.