# Extended Levett trigonometric series

## TL;DR

This paper extends trigonometric series to derive new formulas involving the Hurwitz-Lerch zeta function and special mathematical constants.

## Contribution

The novel contribution is deriving closed-form expressions for extended trigonometric series involving powers of 3 and special functions.

## Key findings

- Closed-form expressions for extended trigonometric series are derived using the Hurwitz-Lerch zeta function.
- New composite finite and infinite series involving special functions and fundamental constants are presented.
- A summary table of interesting results is provided for quick reference.

## 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 and infinite series involving special functions, trigonometric functions and fundamental constants. A short table summarizing some interesting results is produced.