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arXiv · 1211.5033

A closed-form expression for zeta(2n+1) reveals a self-recursive function

Michael A. Idowu
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Abstract

Euler discovered a formula for expressing the value of the Riemann zeta function for all even positive integer arguments. A closed-form expression for the Riemann zeta function for all odd integer arguments, based on the values of the Dirichlet beta function, euler numbers and pi, reveals a new evidence about the self-recursive nature of Riemann zeta function at odd integers. We demonstrate for the first time that the Riemann zeta function at odd integers always produces a recurrence relation that is self-recursive.

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Michael A. Idowu. 2012-11-20. A closed-form expression for zeta(2n+1) reveals a self-recursive function. https://arxiv.org/abs/1211.5033

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