\(k\)-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-Lerch zeta function and Apostol-Bernoulli polynomials

DOI10.1007/s00009-017-1025-4zbMath1404.05010OpenAlexW2762590073MaRDI QIDQ1693363

Abdelmejid Bayad, Yilmaz Simsek, Irem Kucukoglu

Publication date: 31 January 2018

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-017-1025-4

zbMATH Keywords

generating functionStirling numbers of the second kindarithmetical functionLyndon wordsBernoulli numbers and polynomialsnecklacesHurwitz-Lerch zeta functionApostol-Bernoulli numbers and polynomialsspecial numbers and polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Combinatorics on words (68R15) Special sequences and polynomials (11B83) Arithmetic functions; related numbers; inversion formulas (11A25) Hurwitz and Lerch zeta functions (11M35)

Related Items (9)

\(k\)-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-Lerch zeta function and Apostol-Bernoulli polynomials ⋮ Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters ⋮ Combinatorial approach of unified Apostol-type polynomials using \(\alpha \)-distanced words ⋮ Numerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for Apostol-type numbers and polynomials ⋮ On interpolation functions for the number of \(k\)-ary Lyndon words associated with the Apostol-Euler numbers and their applications ⋮ A note on polynomial expressions for sums of power of integers multiplied by exponential terms ⋮ The q-Stirling numbers of the second kind and its applications ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions ⋮ Identities for Dirichlet and Lambert-type series arising from the numbers of a certain special word

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