The Sum of the Series of Reciprocals of the Quadratic Polynomials with Complex Conjugate Roots

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F18%3A00536325" target="_blank" >RIV/60162694:G43__/18:00536325 - isvavai.cz</a>

Výsledek na webu

<a href="http://eiris.it/ojs/index.php/ratiomathematica/issue/view/VOL%2035%20(2018)" target="_blank" >http://eiris.it/ojs/index.php/ratiomathematica/issue/view/VOL%2035%20(2018)</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.23755/rm.v35i0.427" target="_blank" >10.23755/rm.v35i0.427</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Sum of the Series of Reciprocals of the Quadratic Polynomials with Complex Conjugate Roots

Popis výsledku v původním jazyce

This contribution is a follow-up to eight preceding author's papers dealing with the sums of the series of reciprocals of quadratic polynomials with different positive integer roots, with double non-positive integer root, with different negative integer roots, with double positive integer root, with one negative and one positive integer root, with purely imaginary conjugate roots, with integer roots, and with the sum of the finite series of reciprocals of the quadratic polynomials with integer purely imaginary conjugate roots respectively. We deal with the sum of the series of reciprocals of the quadratic polynomials with complex conjugate roots, derive the formula for the sum of these series and verify it by some examples evaluated using the basic programming language of the computer algebra system Maple 16. This contribution can be an inspiration for teachers of mathematics who are teaching the topic Infinite series or as a subject matter for work with talented students.

Název v anglickém jazyce

The Sum of the Series of Reciprocals of the Quadratic Polynomials with Complex Conjugate Roots

Popis výsledku anglicky

This contribution is a follow-up to eight preceding author's papers dealing with the sums of the series of reciprocals of quadratic polynomials with different positive integer roots, with double non-positive integer root, with different negative integer roots, with double positive integer root, with one negative and one positive integer root, with purely imaginary conjugate roots, with integer roots, and with the sum of the finite series of reciprocals of the quadratic polynomials with integer purely imaginary conjugate roots respectively. We deal with the sum of the series of reciprocals of the quadratic polynomials with complex conjugate roots, derive the formula for the sum of these series and verify it by some examples evaluated using the basic programming language of the computer algebra system Maple 16. This contribution can be an inspiration for teachers of mathematics who are teaching the topic Infinite series or as a subject matter for work with talented students.

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

35

Číslo periodika v rámci svazku

2/2018

Stát vydavatele periodika

IT - Italská republika

Počet stran výsledku

11

Strana od-do

75-85

Kód UT WoS článku

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EID výsledku v databázi Scopus

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