ON CERTAIN EDWARDS-TYPE DOUBLE INTEGRALS COMPRISING GENERALIZED HYPERGEOMETRIC FUNCTIONS

ON CERTAIN EDWARDS-TYPE DOUBLE INTEGRALS COMPRISING GENERALIZED HYPERGEOMETRIC FUNCTIONS

This research paper evaluates seven novel master double integrals of Edwards-type containing hypergeometric functions, characterized by various parameters including a general parameter k, which is a natural number. These integrals are evaluated over the region defined by 0 ≤ t ≤ 1 and 0 ≤ y ≤ 1 involving generalized hypergeometric functions _p+1F_p, for p = 3, 4, with argument ${\frac{(1-t)y}{1-ty}}$. These closed-forms are accomplished with the aid of summation formulae established by Masjed-Jamei and Koepf and Edwards double integral. For each master integral, we derive corollaries for specific values of k ∈ {1, 2, 3}, yielding new special integrals. These corollaries enrich the existing body of knowledge and demonstrate our approach's flexibility and wide applicability in generating numerous interesting integrals for any particular value of k. Our main findings extend several established results in the literature.