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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Ratio Mathematica - Journal of Foundations and Applications of Mathematics

ISSN

1592-7415

e-ISSN

2282-8214

Svazek periodika

34

Číslo periodika v rámci svazku

1/2018

Stát vydavatele periodika

IT - Italská republika

Počet stran výsledku

10

Strana od-do

5-14

Kód UT WoS článku

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EID výsledku v databázi Scopus

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