Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F24%3A00558725" target="_blank" >RIV/60162694:G43__/24:00558725 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/book/edit/978-0-7503-5067-9" target="_blank" >https://iopscience.iop.org/book/edit/978-0-7503-5067-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/978-0-7503-5067-9ch1" target="_blank" >10.1088/978-0-7503-5067-9ch1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero

Popis výsledku v původním jazyce

This chapter summarizes and complements the author’s five previous papers dealing with the sums of the series of reciprocals of the cubic polynomials with integer roots involving eight special cases. First, the well-known case of triple zero root is recalled. Further, two cases of a double zero root along with another integer root are stated. The formulas for the sums of the relevant series are combined into a single formula. The next part of the chapter presents two cases of a single zero root and a double integer root. In addition to the sub-formulas, the summary formula for the sum of the relevant series is also given. The final part of the chapter presents three cases of a simple zero root and two different integer roots. In addition to the sub-formulas, the summary formula for the sum of the relevant series is derived. This formula, as in the two previous sections, uses harmonic numbers and an auxiliary sigma-function. This formula is verified by some examples using the computer algebra system Maple. Thus, the series we deal with belong to special types of infinite series which sum are given analytically by means of a relatively simple formula.

Název v anglickém jazyce

Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero

Popis výsledku anglicky

This chapter summarizes and complements the author’s five previous papers dealing with the sums of the series of reciprocals of the cubic polynomials with integer roots involving eight special cases. First, the well-known case of triple zero root is recalled. Further, two cases of a double zero root along with another integer root are stated. The formulas for the sums of the relevant series are combined into a single formula. The next part of the chapter presents two cases of a single zero root and a double integer root. In addition to the sub-formulas, the summary formula for the sum of the relevant series is also given. The final part of the chapter presents three cases of a simple zero root and two different integer roots. In addition to the sub-formulas, the summary formula for the sum of the relevant series is derived. This formula, as in the two previous sections, uses harmonic numbers and an auxiliary sigma-function. This formula is verified by some examples using the computer algebra system Maple. Thus, the series we deal with belong to special types of infinite series which sum are given analytically by means of a relatively simple formula.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Polynomial Paradigms Trends and applications in science and engineering

ISBN

978-0-7503-5067-9

Počet stran výsledku

34

Strana od-do

1-34

Počet stran knihy

382

Název nakladatele

IOP Publishing

Místo vydání

Bristol, United Kingdom

Kód UT WoS kapitoly

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