On certain polylogarithmic double series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On certain polylogarithmic double series

Authors:

Hirofumi Tsumura

Affiliation:

(1) Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

Abstract:

In this paper, we study certain polylogarithmic double series

${sumlimits_{m, n = 1}^infty {frac{{x^{n} }} {{m^{p} n^{q} (m + n)^{r} }}} },{sumlimits_{m, n = 1}^infty {frac{{x^{{m + n}} }} {{m^{p} n^{q} (m + n)^{r} }}} },$

where p, q, r are nonnegative integers and x is any complex number with

. First we give certain polylogarithmic interpolation formulas of the results of Mordell, Subbarao-Sitaramachandrarao and Zagier. By specializing to x = 1, we can obtain their results. Secondly we calculate some special values of these polylogarithmic double series. Received: 21 November 2005; Revised: 8 May 2006

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000). Primary 40B05 Secondary 11M06, 30B99

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