Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

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Austrian Academy of Sciences Press
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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3402-3406, +43-1-512 905-0 Fax +43-1-515 81/DW 3400
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doi:10.1553/etna_vol50s98


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Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access

Irem Kucukoglu, Yilmaz Simsek
S.  98 - 108
doi:10.1553/etna_vol50s98

Open access
doi:10.1553/etna_vol50s98
Abstract:
Because the Lyndon words and their numbers have practical applications in many different disciplines such as mathematics, probability, statistics, computer programming, algorithms, etc., it is known that not only mathematicians but also statisticians, computer programmers, and other scientists have studied them using different methods. Contrary to other studies, in this paper we use methods associated with zeta-type functions, which interpolate the family of Apostol-type numbers and polynomials of order k. Therefore, the main purpose of this paper is not only to give a special power series including the numbers of Lyndon words and binomial coefficients but also to construct new computational algorithms in order to simulate these series by numerical evaluations and plots. By using these algorithms, we provide novel computational methods to the area of combinatorics on words including Lyndon words. We also define new functions related to these power series, Lyndon words counting numbers, and the Apostol-type numbers and polynomials. Furthermore, we present some illustrations and observations on approximations of functions by rational functions associated with Apostol-type numbers that can provide ideas on the reduction of the algorithmic complexity of these algorithms.

Keywords:  Lyndon words, special numbers and polynomials, Apostol-type numbers and polynomials, arithmetical function, interpLyndon words, special numbers and polynomials, Apostol-type numbers and polynomials, arithmetical function, interpolation function, zeta type functionolation function, zeta type function
Published Online:  2019/01/10 14:23:17
Object Identifier:  0xc1aa5576 0x003a3259

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.



Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3402-3406, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at