The simultaneous multiplication formulas for Apostol-Bernoulli polynomials and generalized Frobenius-Euler polynomials
Gennadiy Ilyuta
TL;DR
This paper derives simultaneous multiplication formulas for Apostol-Bernoulli and generalized Frobenius-Euler polynomials, incorporating various Dedekind sums, advancing the theoretical understanding of these special functions.
Contribution
It introduces new multiplication formulas linking Apostol-Bernoulli and Frobenius-Euler polynomials with Dedekind sums.
Findings
Derived simultaneous multiplication formulas for the polynomials.
Connected the formulas with Dedekind-Rademacher, Apostol-Dedekind, and Fourier-Dedekind sums.
Enhanced the theoretical framework of special polynomial functions.
Abstract
We prove the simultaneous multiplication formulas for Apostol-Bernoulli polynomials and generalized Frobenius-Euler polynomials. These formulas contain Dedekind-Rademacher sums, Apostol-Dedekind sums and Fourier-Dedekind sums.
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Taxonomy
TopicsAdvanced Mathematical Identities · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory