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 $$\begin{aligned} \mathcal L=\frac{d^2}{dt^2} + \frac{A'(t)}{A(t)} \frac{d}{dt}, \end{aligned}$$on \((0,\infty )\), where \(A(t)=(\sinh t)^{2\alpha +1}(\cosh t)^{2\beta +1}B(t); \alpha ,\beta > -\frac{1}{2}\) with suitable conditions on B. When \(B\equiv 1\) we get back the Ramanujan’s Master theorem for the Jacobi operator.