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arXiv · 2606.14793

Novel series involving families of zeta functions and special functions and polynomials by applying Norlund sum and derivative formula

Elif Sukruoglu·Yilmaz Simsek
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Abstract

In recent years, the Norlund sum and its applications have attracted considerable attention, especially in mathematics and other applied sciences. Because this sum plays an important role in mathematical modeling involving differential equations and difference equations, as well as in the theory of infinite series and integral transforms. Therefore, one of the most important goals of this article is to present a new approach to generating function and to derive new formulas including the sum of (inverse) Laplace transforms, the Norlund sum, the alternative Hurwitz zeta function, and the inverse Catalan sum formula with related operators. Another aim is to establish the relationship between the inverse Catalan sum formula and the derivative operator, and to give new formulas and relations, including the zeta function, the Bernoulli numbers, and the Laplace transform. Furthermore, applications are given including the relationship between these operators and the Dirichlet L-function. Some new formulas for certain classes of infinite series, including the Dirichlet L-function, the zeta function, Euler numbers of the second kind, and the Apostol-Bernoulli polynomials of higher-order.

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Elif Sukruoglu, Yilmaz Simsek. 2026-06-11. Novel series involving families of zeta functions and special functions and polynomials by applying Norlund sum and derivative formula. https://arxiv.org/abs/2606.14793

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