Dixit, AtulAtulDixitKumar, RahulRahulKumar2025-08-312025-08-312022-01-0110.46298/hrj.2023.109132-s2.0-85164402969https://d8.irins.org/handle/IITG2025/27139A modular relation of the form F (α, w) = F (β, iw), where i =^√−1 and αβ = 1, is obtained. It involves the generalized digamma function ψ<inf>w</inf>(a) which was recently studied by the authors in their work on developing the theory of the generalized Hurwitz zeta function ζ<inf>w</inf>(s, a). The limiting case w → 0 of this modular relation is a famous result of Ramanujan on page 220 of the Lost Notebook. We also obtain asymptotic estimate of a general integral involving the Riemann function Ξ(t) as α → ∞. Not only does it give the asymptotic estimate of the integral occurring in our modular relation as a corollary but also some known results.trueasymptotic estimates | Generalized digamma function | Generalized Hurwitz zeta function | modular relation | Ramanujan’s Lost notebookArticlehttps://hrj.episciences.org/10913/pdf28047370140-15120222arJournal0