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The proof of a formula concerning the asymptotic behavior of the reciprocal sum of the square of multiple-angle Fibonacci numbers

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50018995" target="_blank" >RIV/62690094:18470/22:50018995 - isvavai.cz</a>

  • Result on the web

    <a href="https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-022-02755-7" target="_blank" >https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-022-02755-7</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1186/s13660-022-02755-7" target="_blank" >10.1186/s13660-022-02755-7</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The proof of a formula concerning the asymptotic behavior of the reciprocal sum of the square of multiple-angle Fibonacci numbers

  • Original language description

    Let (F-n)(n) be the Fibonacci sequence defined by Fn+2 = Fn+1 + F-n with F-0 = 0 and F-1 = 1. In this paper, we prove that for any integer m &gt;= 1 there exists a positive constant C-m for which lim(n -&gt;infinity){(Sigma(infinity)(k=n)1/F-mk(2))(-1) - (F-mn(2)-F-m(n-1)(2) + (-1)C-mn(m))} = 0. Furthermore, we show that C-m tends to 2/5 as m -&gt;infinity (indeed, we provide quantitative versions of the previous results as well as an explicit form for C-m). This confirms some questions proposed by Lee and Park [J. Inequal. Appl. 2020(1):91 2020].

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Inequalities and Applications

  • ISSN

    1029-242X

  • e-ISSN

    1029-242X

  • Volume of the periodical

    2022

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    16

  • Pages from-to

    "Article Number: 21"

  • UT code for WoS article

    000749201300001

  • EID of the result in the Scopus database

    2-s2.0-85123985102