On Eulerian Log-Gamma Integrals and Tornheim–Witten Zeta Functions
نویسندگان
چکیده
Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate
منابع مشابه
Computation and theory of Mordell-Tornheim-Witten sums II
In [7] the current authors, along with the late and much-missed Richard Crandall (1947– 2012), considered generalized Mordell–Tornheim–Witten (MTW) zeta-function values along with their derivatives, and explored connections with multiple-zeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function th...
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We consider some fundamental generalized Mordell–Tornheim–Witten (MTW) zeta-function values along with their derivatives, and explore connections with multiplezeta values (MZVs). To achieve this, we make use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. Our original motivation was to represent unresolved constructs...
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Firstly, we prove a functional relation for the Tornheim double zeta function. Using this functional relation, we obtain simple proofs of some known formulas for special values of Tornheim and Euler-Zagier double zeta functions. Secondly, we obtain functional relations for Witten zeta functions by using a double L-values relation. By these functional relations, we obtain new proofs of known res...
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تاریخ انتشار 2012