Dixit, AtulAtulDixitGupta, R.R.Gupta2025-08-312025-08-312019-09-0110.1016/j.aam.2019.06.0032-s2.0-85068258100https://d8.irins.org/handle/IITG2025/23202A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for ζ(2m+1). The formula for ζ²(2m+1) is then generalized in two different directions, one, by considering the generalized divisor function σ<inf>z</inf>(n), and the other, by studying a more general analogue of the aforementioned Eisenstein series, consisting of one more parameter N. A number of important special cases are derived from the first generalization. For example, we obtain a series representation for ζ(1+ω)ζ(−1−ω), where ω is a non-trivial zero of ζ(z). We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of ζ(4k−1) and ζ(4k+1) for k∈N.trueDedekind eta function | Irrationality | Modified Bessel function | Odd zeta values | Ramanujan's formulaArticle1090207486-119September 20196arJournal6WOS:000484874000005