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The aim of the present paper is to give unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions. It is a unification and generalization of certain families of elliptic-type integrals which were studied in a number of earlier works on the subject due to their importance and potential in certain problems in radiation physics and nuclear technology. The results established in this paper are of manifold generality and basic in nature. Besides deriving various known and new elliptic-type integrals and their generalizations these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions

Unified presentation of certain families of elliptic-type integrals related to Euler integrals and generating functions