TL;DR
This paper extends the Watson-Harkins sum to derive finite sums involving generalized Hurwitz-Lerch Zeta functions, introduces transformation formulas, and derives finite products of trigonometric functions, all presenting new mathematical results.
Contribution
The paper introduces new extensions of the Watson-Harkins sum and derives novel finite sums and products involving generalized Hurwitz-Lerch Zeta functions.
Findings
Finite sum expressions in terms of Hurwitz-Lerch Zeta functions.
Transformation formulas for various parameter values.
New finite products of trigonometric functions.
Abstract
The Watson-Harkins sum involving the product of the cosine and cosecant functions is extended to derive the finite sum of generalized Hurwitz-Lerch Zeta functions is derived in terms of the Hurwitz-Lerch Zeta function. A transformation formula arises for various finite values of the parameters involved. The finite product of trigonometric functions are also derived. All the results in this work are new.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Inequalities and Applications · Advanced Mathematical Identities