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Multiple harmonic series related to multiple Euler numbers

โœ Scribed by Hirofumi Tsumura

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
248 KB
Volume
106
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values.

๐Ÿ“œ SIMILAR VOLUMES

Multiplicative Relations in Powers of Eu
Multiplicative Relations in Powers of Euler's Product
โœ Scott Ahlgren ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 133 KB

In a recent paper, Cooper, Hirschhorn, and Lewis conjecture many relations among the coefficients of certain products of powers of Euler's product. Here we use the theory of modular forms with complex multiplication to prove these conjectures.

Summing one- and two-dimensional series
Summing one- and two-dimensional series related to the Euler series
โœ Odd Magne Ogreid; Per Osland ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 1002 KB

We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in terms of ((2), ((3), the Catalan constant G and C12(~/3) where