Analytic continuation for multiple zeta values using symbolic representations
| Autor: | Christophe Vignat, Tanay Wakhare, Lin Jiu |
|---|---|
| Přispěvatelé: | Department of Mathematics [Tulane, New Orleans], Tulane University, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, University of Maryland |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Mathematics - Number Theory Analytic continuation 010102 general mathematics Representation (systemics) Harmonic (mathematics) 010103 numerical & computational mathematics 16. Peace & justice Symbolic computation 01 natural sciences Algebra [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] FOS: Mathematics Number Theory (math.NT) 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | International Journal of Number Theory International Journal of Number Theory, World Scientific Publishing, 2020, 16 (03), pp.579-602. ⟨10.1142/S1793042120500293⟩ |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042120500293⟩ |
| Popis: | We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these sums. This approach is also applied to the study of the family of extended Bernoulli polynomials, which appear in the computation of harmonic sums at negative indices. It also allows us to reinterpret the Raabe analytic continuation of the multiple zeta function as both a constant term extension of Faulhaber's formula, and as the result of a natural renormalization procedure for Faulhaber's formula. Comment: 22 pages, comments are welcome |
| Databáze: | OpenAIRE |
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