Multiplication and Inversion Formulas for Higher-Order Lerch Zeta Functions with Polynomial Coefficients
Year: 2026
Type: article
Abstract: We consider the $N$-tuple Hurwitz-Lerch zeta function introduced by Srivastava and Choi, ζN(s,x,λ)=∑k1,…,kN≥0λk1+⋯+kN(x+k1+⋯+kN)s, where $N$ is a positive integer and $\lambda$ is a complex parameter. Using polynomial coefficients, we derive multiplication and inversion formulas for this function. We further investigate these coefficients and prove symmetry relations, finite-difference identities, recurrence formulas, and unimodality, together with integral representations and asymptotic behavior. As applications, we obtain new identities for higher–order Apostol–Euler and Apostol–Bernoulli polynomials. Our results unify and extend several known formulas.
Source: Mathematics
DOI: 10.3390/math14183264
Authors: Damla Gun, Abdelmejid Bayad, Yilmaz Simsek
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7212054399