The Evaluation of Tornheim Double Sums. Part 2
نویسندگان
چکیده
We provide an explicit formula for the Tornheim double series T (a, 0, c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a = m, c = n, we show that in the most interesting case of even weight N := m + n the Tornheim sum T (m, 0, n) can be expressed in terms of zeta values and the family of integrals
منابع مشابه
ar X iv : 0 81 1 . 05 57 v 1 [ m at h . N T ] 4 N ov 2 00 8 THE EVALUATION OF TORNHEIM DOUBLE SUMS . PART 2
We provide an explicit formula for the Tornheim double series T (a, 0, c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a = m, c = n, we show that in the most interesting case of even weight N := m + n the Tornheim sum T (m, 0, n) can be expressed in terms of zeta values and the family of integrals
متن کاملThe Evaluation of Tornheim Double Sums
We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be expressed in terms of definite integrals of triple products of Bernoulli polynomials and the Bernoulli function Ak(q) := kζ(1− k, q).
متن کاملSIGNED q-ANALOGS OF TORNHEIM’S DOUBLE SERIES
We introduce signed q-analogs of Tornheim’s double series and evaluate them in terms of double q-Euler sums. As a consequence, we provide explicit evaluations of signed and unsigned Tornheim double series and correct some mistakes in the literature.
متن کاملOn Evaluations of Infinite Double Sums and Tornheim’s Double Series
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 evalua...
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 کامل