Functions and Analysis

    

Expansion of the Number π Into a Series of Trigonometric Functions and Its Connection with the Riemann Zeta Function

Authors: Bohdan Dykyi

In this work, series expansions for negative and positive integer powers of the number π are derived using Viète’s infinite product and differentiation techniques. A representation of these powers in terms of trigonometric series involving tangent functions is obtained. Furthermore, a connection between these expansions and the values of the Riemann zeta function at even arguments is established. Explicit formulas for the reciprocal values of the zeta function are presented. Several illustrative examples are provided.

Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)

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[v1] 2026-02-05 20:19:16

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