An operational calculus generalization of Ramanujan's master theorem

We give a formal extension of Ramanujan's master theorem using operational methods. The resulting identity transforms the computation an integral product on half-line to Laplace transform. Since is purely formal, we show consistency this approach with various standard calculus results, followed by several examples, including Feynman diagram evaluation, illustrate power extension. then briefly discuss connection between and identities Hardy Carr before extending latter in same way extended Ramanujan's. Finally, generalize our producing additional interesting as corollary.