Sum of generalized alternating harmonic series with three periodically repeated numerators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F15%3A00531637" target="_blank" >RIV/60162694:G43__/15:00531637 - 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
<a href="http://dx.doi.org/10.15414/meraa.2015.01.02.42-48" target="_blank" >10.15414/meraa.2015.01.02.42-48</a>

Result language
angličtina
Original language name
Sum of generalized alternating harmonic series with three periodically repeated numerators
Original language description
This contribution deals with the generalized convergent harmonic series with three periodically repeated numerators; i. e. with periodically repeated numerators (1,a,b), where a,b are real numbers. Firstly, it is derived that the only value of the coefficient b, for which this series converges, is b=-a-1. Then the formula for the sum s(a) of this series is analytically derived. A relation for calculation the value of the real constant a from an arbitrary sum s(a) also follows from the derived formula. The obtained analytical results are finally numerically verified by using the computer algebra system Maple 15 and its basic programming language.
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
KA - Militarism
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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