In this paper, we obtain an analytical solution for an unsolved definite integral R C ( m , n ) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral R C ( m , n ) defined in terms of the ordinary hypergeometric function ₂F₃ with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions ₀F₁ , ₁F₂ and ₂F₃.

Keywords: generalized hypergeometric function, infinite Fourier cosine transforms, Ramanujan’s integrals, Fox-Wright psi hypergeometric function, Mellin transforms, series decomposition identity, bounded sequence