Extended Levett trigonometric series

TL;DR

This paper extends finite trigonometric series involving geometric angles to derive closed-form formulas with the Hurwitz-Lerch zeta function, enabling new expressions for series with special functions and constants.

Contribution

It introduces novel closed-form formulas for extended trigonometric series involving the Hurwitz-Lerch zeta function, expanding analytical tools for series involving geometric angles.

Findings

Derived closed-form expressions involving the Hurwitz-Lerch zeta function.

Presented a table summarizing key results and formulas.

Connected trigonometric series with special functions and constants.

Abstract

An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3. These closed formulae are used to derive composite finite series involving special functions, trigonometric functions and fundamental constants. A short table summarizing some interesting results is produced.