Gün D., Bayad A., Şimşek Y.
MATHEMATICS, vol.14, no.18, pp.1-18, 2026 (SCI-Expanded, Scopus)
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Publication Type:
Article / Article
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Volume:
14
Issue:
18
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Publication Date:
2026
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Doi Number:
10.3390/math14183264
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Journal Name:
MATHEMATICS
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Journal Indexes:
Academic Search Ultimate (EBSCO), Scopus, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest), Aerospace Database, Science Citation Index Expanded (SCI-EXPANDED), zbMATH, Directory of Open Access Journals
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Page Numbers:
pp.1-18
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Akdeniz University Affiliated:
Yes
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 λ is a complex parameter. A central breakthrough in this work is the explicit reduction of the N-tuple function to a linear combination of single Lerch transcendents via a finite-difference identity, which naturally leads to sharp multiplication and inversion formulas. We further investigate the combinatorial structure of the underlying polynomial coefficients, establishing their symmetry, unimodality, log-concavity, and precise asymptotic behavior. As key applications, we derive new identities for higher-order Apostol-Euler and Apostol-Bernoulli polynomials. Our results unify and extend several known formulas.