Computation and theory of extended Mordell-Tornheim-Witten sums
نویسندگان
چکیده
منابع مشابه
Computation and theory of extended Mordell-Tornheim-Witten sums
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...
متن کاملComputation 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...
متن کاملComputation and experimental evaluation of Mordell–Tornheim–Witten sum derivatives
In previous work the present authors and others have studied Mordell-Tornheim-Witten sums and their connections with multiple-zeta values. In this note we describe the numerical computation of derivatives at zero of a specialization originating in a preprint by Romik, and the experimental evaluation of these numerical values in terms of well-known constants.
متن کاملComputation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums
This paper extends tools developed in [10, 8] to study character polylogarithms. These objects are used to compute Mordell-Tornheim-Witten character sums and to explore their connections with multiple-zeta values (MZVs) and with their character analogues [17].
متن کاملComputation of the Mordell-tornheim Zeta Values
In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values: ζMT,r(s1, · · · , sr ; s) := ∞ ∑ m1, ··· ,mr=1 1 m1 1 · · ·m sr r (m1 + · · ·+mr)s for the special cases ζMT,r(1, · · · , 1; s) and ζMT,r(0, · · · , 0; s). Some interesting (known or new) consequences and illustrative examples are also considered.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02768-3