A unified elliptic-type integral and associated recurrence relations

Elliptic-type integrals have their importance or potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of elliptic-type integrals. Beside explicit representations of certain families of unified elliptic-type integrals, contour integral representation, various recurrence relations are derived in the present investigation. The results derived in this article are of manifold generality and provide extensions and unification to the large number of known results established earlier.