Extensions of Watson’s theorem and the Ramanujan–Guinand formula

Ramanujan provided several results involving the modified Bessel function [Formula: see text] in his Lost Notebook. One of them is famous Ramanujan–Guinand formula, equivalent to functional equation non-holomorphic Eisenstein series on SL[Formula: text]. Recently, this formula was generalized by Dixit, Kesarwani, and Moll. In paper, we first obtain a generalization theorem Watson and, as an application it, give new proof result Watson’s also different direction using which itself Analytic continuation all these are given.