The sum of the reduced harmonic series generated by four primes determined analytically and computed by using CAS Maple

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F13%3A00499103" target="_blank" >RIV/60162694:G43__/13:00499103 - isvavai.cz</a>
Result on the web
<a href="http://vavtest.unob.cz/registr" target="_blank" >http://vavtest.unob.cz/registr</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The sum of the reduced harmonic series generated by four primes determined analytically and computed by using CAS Maple
Original language description
The paper deals with the reduced harmonic series generated by four primes. A formula for the sum of these convergent reduced harmonic series is derived. These sums (concretely 42 from all 12650 sums generated by four different primes smaller than 100) are computed by using the computer algebra system Maple 15 and its programming language, although the formula is valid not only for four arbitrary primes, but also for four integers. We can say that the reduced harmonic series generated by four primes (orby four integers) belong to special types of convergent infinite series, such as geometric and telescoping series, which sum can be found analytically by means of a simple formula.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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