On certain double integrals involving generalized hypergeometric functions and logarithmic powers

In this paper, we evaluate certain novel double integrals that incorporate generalized hypergeometric functions and powers of the logarithmic functions, which are formulated using classical functions such as the Gamma function, Psi function, and Hurwitz zeta functions. These integrals are derived by utilizing advanced techniques such as series expansions and logarithmic differentiation. The double integrals are represented using the $n$-th derivative expressions of the gamma function ratios. A well-known double integral due to Edwards serves as a key foundation for deriving the results presented in this work.