Evaluation of Spannenintegrals of the product of zeta-functions.

It has been pointed out by Li, Hashimoto and Kanemitsu [Ito, T., 2006, On an integral representation of special values of the zeta function at odd integers. Journal of the Mathematical Society of Japan, 58, 681-691.] that the recent result of Ito [Li, H.-L., Hashimoto, M. and Kanemitsu, S., 2007, Examples of the Hurwitz transforms, in press.] is example 5.2 of Espinosa and Moll [Mikolás, M., 1957, A simple proof of the functional equation for the Riemann zeta-function and a forumula of Hurwitz. Acta Scientiarum Mathematicarum (Szeged), 18, 261-263.], whose main results in turn are contained in a more anteceding deep result of Mikolás [Nakamura, T., 2006, A functional relation for the Tornheim double zeta function. Acta Arithmetica, 125, 257-263.]. In this paper, we shall clarify the situation more completely and give some further results, from the point of view of application of the functional equation. [ABSTRACT FROM AUTHOR]