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An Alternative Approach to Computing $\beta(2k+1)$ by Tanabe, Naomi; Wattanawanichkul, Nawapan is a scholarly article available to read on EtoBox.

What is An Alternative Approach to Computing $\beta(2k+1)$ about?

This paper presents a new approach to evaluating the special values of the Dirichlet beta function, $\beta(2k+1)$, where $k$ is any nonnegative integer. Our approach relies on some properties of the Euler numbers and polynomials, and uses basic calculus and telescoping series. By a similar procedure, we also yield an integral representation of $\beta(2k)$. The idea of our proof adapts from a previous study by Ciaurri et al., where the authors introduced a new proof of Euler's formula for $\zeta(2k)$.

Author

Tanabe, Naomi; Wattanawanichkul, Nawapan

Published

2023

Language

EN