Ramanujan’s master theorem for sturm liouville operator

Abstract

In this paper we prove an analogue of the Ramanujan’s master theorem in the setting of Sturm Liouville operator L = d2/dt2 + A'(t) /A(t).d/dt , on (0,∞), where A(t) = (sinh t)2α+1(cosh t)2β+1B(t); α, β > −1 2 with suitable conditions on B. When B ≡ 1 we get back the Ramanujan’s Master theorem for the Jacobi operator.