Hurwitz--Lerch Type Families of Poly-Bernoulli and Poly-Cauchy Numbers and Polynomials with Parameters (α,a)

2025/08/09 by Lacpao, Noel B., Corcino, Roberto B.
#05A19 #11B68 #11B73 #11B83 #11M35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.06766

Abstract

This study introduces (α,a)-parameterized Hurwitz-Lerch type poly-Bernoulli and poly-Cauchy numbers and polynomials, extending classical sequences through the Hurwitz-Lerch zeta function. We derive generating functions, recurrences, and explicit formulas, revealing deeper structures and connections with zeta functions and polylogarithms. The results enrich existing theory and open new directions in analytic number theory and combinatorics.

Citations

• Some relations of two type 2 polymomilas and discrete harmonic numbers and polynomials
• A note on new type degenerate Bernoulli numbers
• A note on type 2 Changhee and Daehee polynomials
• A note on degenerate Stirling numbers of the first kind
• Extended stirling polynomials of the second kind and extended Bell polynomials
• A New approach to q-zeta function

Related

• Recurrences for values of the Hurwitz type poly-Bernoulli numbers and polynomials
• Multiparameter poly-Cauchy and poly-Bernoulli numbers and polynomials
• On Multi Poly-Bernoulli Polynomials
• Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers
• Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers