Multiplication and Inversion Formulas for Higher-Order Lerch Zeta Functions with Polynomial Coefficients


Gün D., Bayad A., Şimşek Y.

MATHEMATICS, cilt.14, sa.18, ss.1-18, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 18
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/math14183264
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: 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
  • Sayfa Sayıları: ss.1-18
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.