Extended Levett trigonometric series
Robert Reynolds
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.
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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Analytic Number Theory Research