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Zbl 0969.11030
Choi, Junesang; Srivastava, H.M.
Certain classes of series associated with the zeta function and multiple gamma functions. (English)
[J] J. Comput. Appl. Math. 118, No.1-2, 87-109 (2000). ISSN 0377-0427

The authors apply the theory of multiple Gamma functions, which was recently reviewed in the study of the determinants of Laplacians, in order to evaluate some families of series involving the Riemann zeta-function. By introducing a (presumably new) mathematical constant, they also systematically evaluate this constant and some definite integrals of the triple Gamma function. Various classes of series associated with the zeta function, some of which can also be used to compute the determinant of the Laplacian on the four-dimensional unit sphere $S^4$ explicitly, are expressed in closed forms.
[H.M.Srivastava (Victoria)]

MSC 2000:: *11M06 Riemannian zeta-function and Dirichlet L-function
33B15 Gamma-functions, etc.

Keywords: multiple Gamma functions; Riemann zeta-function; constant; definite integrals; determinant of the Laplacian

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