A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ Method
Abstract
By using the related results in the WZ theory, a new (as far as I know) formula for the values of Dirichlet beta function $\beta (s) = \sum\limits_{n = 1}^{+ \infty} {\frac{(-1)^{n - 1}}{(2n - 1)^s}} $ (where $Re(s) > 0$) at odd positive integers was given.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2012
- DOI:
- 10.48550/arXiv.1211.3149
- arXiv:
- arXiv:1211.3149
- Bibcode:
- 2012arXiv1211.3149C
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Classical Analysis and ODEs;
- 05A19
- E-Print:
- 13 pages