Formulas for the Sums of the Series of Reciprocals of the Polynomial of Degree Two with Non-zero Integer Roots

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F21%3A00556641" target="_blank" >RIV/60162694:G43__/21:00556641 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-030-61334-1_18" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-030-61334-1_18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-61334-1_18" target="_blank" >10.1007/978-3-030-61334-1_18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Formulas for the Sums of the Series of Reciprocals of the Polynomial of Degree Two with Non-zero Integer Roots

Popis výsledku v původním jazyce

This chapter deals with the sums of the series of reciprocals of the quadratic polynomials with non-zero integer roots. It is a follow-up and a completion to the previous author’s papers dealing with the sums of these series, where the quadratic polynomials have all possible types of positive and negative integer roots. First, the conditions for the coefficients of a reduced quadratic equation are given so that this equation has only integer roots. Further, summary formulas for the sums of the series of reciprocals of the quadratic polynomials with non-zero integer roots are stated and derived. These formulas are verified by some examples using the basic programming language of the computer algebra system Maple. The series we deal with so belong to special types of infinite series which sums are given analytically by simple formulas.

Název v anglickém jazyce

Formulas for the Sums of the Series of Reciprocals of the Polynomial of Degree Two with Non-zero Integer Roots

Popis výsledku anglicky

This chapter deals with the sums of the series of reciprocals of the quadratic polynomials with non-zero integer roots. It is a follow-up and a completion to the previous author’s papers dealing with the sums of these series, where the quadratic polynomials have all possible types of positive and negative integer roots. First, the conditions for the coefficients of a reduced quadratic equation are given so that this equation has only integer roots. Further, summary formulas for the sums of the series of reciprocals of the quadratic polynomials with non-zero integer roots are stated and derived. These formulas are verified by some examples using the basic programming language of the computer algebra system Maple. The series we deal with so belong to special types of infinite series which sums are given analytically by simple formulas.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Algorithms as a Basis of Modern Applied Mathematics

ISBN

978-3-030-61333-4

Počet stran výsledku

20

Strana od-do

363-382

Počet stran knihy

509

Název nakladatele

Springer Nature Switzerland AG

Místo vydání

Cham, Switzerland

Kód UT WoS kapitoly

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