Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero
Original language description
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.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Polynomial Paradigms Trends and applications in science and engineering
ISBN
978-0-7503-5067-9
Number of pages of the result
34
Pages from-to
1-34
Number of pages of the book
382
Publisher name
IOP Publishing
Place of publication
Bristol, United Kingdom
UT code for WoS chapter
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