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Sums of Generalized Harmonic Series with Periodically Repeated Numerators (a,b) and (a,a,b,b)

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F18%3A00535271" target="_blank" >RIV/60162694:G43__/18:00535271 - isvavai.cz</a>

  • Result on the web

    <a href="http://eiris.it/ojs/index.php/ratiomathematica/issue/view/55" target="_blank" >http://eiris.it/ojs/index.php/ratiomathematica/issue/view/55</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.23755/rm.v34i0.405" target="_blank" >10.23755/rm.v34i0.405</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Sums of Generalized Harmonic Series with Periodically Repeated Numerators (a,b) and (a,a,b,b)

  • Original language description

    This paper deals with certain generalization of the alternating harmonic series - the generalized convergent harmonic series with periodically repeated numerators (a,b) and (a,a,b,b). Firstly, we find out the value of the numerators b of the first series, for which the series converges, and determine the formula for the sum s(a) of this series. Then we determine the value of the numerators b of the second series, for which this series converges, and derive the formula for the sum s(a,a) of this second series. Finally, we verify these analytically obtained results and compute the sums of these series by using the computer algebra system Maple 16 and its basic programming language.

  • Czech name

    —

  • Czech description

    —

Classification

  • Type

    J<sub>ost</sub> - Miscellaneous article in a specialist periodical

  • CEP classification

    —

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    —

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2018

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Ratio Mathematica - Journal of Foundations and Applications of Mathematics

  • ISSN

    1592-7415

  • e-ISSN

    2282-8214

  • Volume of the periodical

    34

  • Issue of the periodical within the volume

    1/2018

  • Country of publishing house

    IT - ITALY

  • Number of pages

    10

  • Pages from-to

    5-14

  • UT code for WoS article

    —

  • EID of the result in the Scopus database

    —

Similar results(10)

Sums of Generalized Convergent Harmonic Series with Periodically Repeated Numerators (1,a,b)Sum of generalized alternating harmonic series with three periodically repeated numeratorsSums of Generalized Alternating Harmonic Series with Periodically Repeated Numerators (1,a) and (1,1,a)