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On MordellTornheim sums and multiple zeta values
, 2010
"... We prove that any MordellTornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, it follows that any MordellTornheim sum with weight and depth of opposite parity can be expressed ..."
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We prove that any MordellTornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, it follows that any MordellTornheim sum with weight and depth of opposite parity can be expressed as a rational linear combination of products of multiple zeta values of lower depth.
Computation and structure of character polylogarithms with applications to character . . .
, 2014
"... ..."
On the Summability of Bivariate Rational Functions
, 2012
"... We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of val ..."
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We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated, first, in terms of single sums and, finally, in terms of values of special functions.
Using Carsten Schneider’s software Sigma the following result was obtained by Pemantle
"... ABSTRACT. We consider generalizations of a sum, which was recently analyzed by Pemantle and Schneider using the computer software Sigma, and later also by Panholzer and Prodinger. Our generalizations include Tornheim’s double series as a special case. We also consider alternating analogs of Tornheim ..."
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ABSTRACT. We consider generalizations of a sum, which was recently analyzed by Pemantle and Schneider using the computer software Sigma, and later also by Panholzer and Prodinger. Our generalizations include Tornheim’s double series as a special case. We also consider alternating analogs of Tornheim’s series. For Tornheim’s double series and its alternating counterparts we provide short proofs for evaluation formulas, which recently appeared in the literature. We introduce finite Tornheim double sums and alternating analogs, and provide relations to finite multiple zeta functions, similarly to the infinite case. Besides, we discuss the evaluation of another double series, which also