Abstract :
We proveimage where image is the zeta-regularized product of the sequence {an}n and Γ(z) is Eulerʹs gamma function. As a part of our result, we obtain the formula of Lerch, Kurokawa and Wakayama. Moreover this result gives an example of a pair of sequences {an},{bn} which satisfies image, although this equality does not hold in general. We also give two-dimensional analogue and q-analogue of our result. Barnesʹ double gamma functions and Jacksonʹs q-gamma functions appear instead of Eulerʹs gamma function Γ(z).
