Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables

Asymptotic expansions for a class of generalized holomorphic Eisenstein series, Ramanujan's formula for $ζ(2k+1)$, Weierstrass' elliptic and allied functions

“…both as z → 0 and z → ∞ through H + . It has fairly recently been shown by the authors [13] that complete asymptotic expansions exist for a two variable analogue of F (s; z), when the associated parameters z = (z 1 , z 2 ) vary within the polysector (H ± ) 2 , so as that the distance |z 2 − z 1 | becomes both small and large. The paper is organized as follows.…”

Integrals of products of Hurwitz zeta functions via Feynman parametrization and two double sums of Riemann zeta functions

“…It is hoped that this approach can be successfully exploited to deal with other integrals or sums of a similar nature. As possible candidates we note here the mean square integrals reviewed in [18], integrals involving products of the alternating counterpart to the Hurwitz zeta function [8] and double Eisenstein series studied very recently in [19].…”