Numerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for Apostol-type numbers and polynomials

DOI10.1553/ETNA_VOL50S98zbMath1477.68253OpenAlexW2910567726MaRDI QIDQ1716849

Yilmaz Simsek, Irem Kucukoglu

Publication date: 5 February 2019

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol50/abstract.php?vol=50&pages=98-108

zbMATH Keywords

interpolation functionarithmetical functionLyndon wordsspecial polynomialsspecial numbersApostol-type numbersApostol-type polynomialszeta-type function

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Combinatorics on words (68R15) Number-theoretic algorithms; complexity (11Y16) Special sequences and polynomials (11B83) Arithmetic functions; related numbers; inversion formulas (11A25) Zeta functions and (L)-functions (11S40) Numerical aspects of recurrence relations (65Q30)

Related Items (2)

A new class of generalized Fubini polynomials and their computational algorithms ⋮ Applications of Apostol-type numbers and polynomials: approach to techniques of computation algorithms in approximation and interpolation functions

Cites Work

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• Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials
• \(q\)-Bernoulli numbers and polynomials associated with multiple \(q\)-zeta functions and basic \(L\)-series
• The origins of combinatorics on words
• \(k\)-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-Lerch zeta function and Apostol-Bernoulli polynomials
• Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions
• On the Lerch zeta function
• Computation methods for combinatorial sums and Euler-type numbers related to new families of numbers
• ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS
• A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials

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