- Title
- Computation and theory of extended Mordell-Tornheim-Witten sums
- Creator
- Bailey, David; Borwein, Jonathan; Crandall, Richard
- Relation
- Mathematics of Computation Vol. 83, Issue 288, p. 1795-1821
- Relation
- http://www.ams.org/journals/mcom/2014-83-288/S0025-5718-2014-02768-3
- Publisher
- American Mathematical Society (AMS)
- Resource Type
- journal article
- Date
- 2014
- Description
- We consider some fundamental generalized Mordell-Tornheim-Witten (MTW) zeta-function values along with their derivatives, and explore connections with multiple-zeta values (MZVs). To achieve this, we make use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. Our original motivation was to represent unresolved constructs such as Eulerian log-gamma integrals. We are able to resolve all such integrals in terms of an MTW basis. We also present, for a substantial subset of MTW values, explicit closed-form expressions. In the process, we significantly extend methods for high-precision numerical computation of polylogarithms and their derivatives with respect to order.
- Subject
- Mordell-Tornheim-Witten; computation; combinatorics; numerical integration
- Identifier
- http://hdl.handle.net/1959.13/1042663
- Identifier
- uon:14096
- Identifier
- ISSN:0025-5718
- Rights
- First published in Mathematics of Computation in Volume 83, Number 288, 2014, published by the American Mathematical Society.
- Language
- eng
- Reviewed
- Hits: 2554
- Visitors: 3040
- Downloads: 217
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Publisher version (open access) | 1 MB | Adobe Acrobat PDF | View Details Download |