Abstract:
A 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 . The formula for is then generalized in two different directions, one, by considering the generalized divisor function , 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 , where ? is a non-trivial zero of . We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of and for .