A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ Method

preprint2012arXivOpen access

By using the related results in the WZ theory, a new (as far as I know) formula for the values of Dirichlet beta function $β(s) = \sum\limits_{n = 1}^{+ \infty} {\frac{(-1)^{n - 1}}{(2n - 1)^s}}$ (where $Re(s) > 0$ ) at odd positive integers was given.

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A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ Method

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