Euler sums and integrals of polylogarithm functions
| Autor: | Yuhuan Yan, Zhijuan Shi, Ce Xu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Polylogarithm Computation 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS TheoryofComputation_GENERAL Proof of the Euler product formula for the Riemann zeta function 01 natural sciences Riemann zeta function Cauchy product 010101 applied mathematics Algebra symbols.namesake Simple (abstract algebra) TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Euler's formula Order (group theory) 0101 mathematics MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | Journal of Number Theory. 165:84-108 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2016.01.025 |
| Popis: | This paper develops an approach to evaluation of Euler sums and integrals of polylogarithm functions. The approach is based on simple Cauchy product formula computations. Using the approach, some relationships between Euler sums and integrals of polylogarithm functions are established. A kind of seven, eight and nine order sums of Euler sums are obtained. Furthermore, we give explicit formula for several classes of Euler sums and integrals of polylogarithm functions in terms of Riemann zeta values. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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