Berndt, Bruce C.Bruce C.BerndtDixit, AtulAtulDixitGupta, RajatRajatGuptaZaharescu, AlexandruAlexandruZaharescu2025-08-282025-08-282021-12-01http://arxiv.org/abs/2112.09819https://d8.irins.org/handle/IITG2025/20092The neglected Russian mathematician, N.~S.~Koshliakov, derived beautiful generalizations of the classical Abel--Plana summation formula through a setting arising from a boundary value problem in heat conduction. When we let the parameter p in this setting tend to infinity, his formulas reduce to the classical Abel--Plana summation formula. Rigorous formulations and proofs of these summation formulas are given. In his notebooks, Ramanujan derived different analogues of the Abel--Plana summation formula. One particular example provides a vast new generalization of the classical transformation formula for Eisenstein series, which we generalize in Koshliakov's setting.en-USClassical Abel-Plana summation formulaKoshliakov's setting.e-Printe-Print123456789/555