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Pré-Publication, Document De Travail Année : 2018

Series Representation of Power Function

Résumé

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers $m=5,7$ as row items sum and generalized obtained results in order to receive every odd-powered monomial $n^{2m+1}, \ m\geq0$ as sum of row terms of corresponding triangle. This version might be out of date, proceed by the $\href{https://kolosovpetro.github.io/series_representation_of_power_function/}{\mathrm{link}}$ to see actual version.
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Dates et versions

hal-01283042 , version 1 (04-03-2016)
hal-01283042 , version 2 (08-04-2016)
hal-01283042 , version 3 (01-07-2016)
hal-01283042 , version 4 (08-03-2017)
hal-01283042 , version 5 (06-05-2017)
hal-01283042 , version 6 (01-08-2017)
hal-01283042 , version 7 (03-12-2017)
hal-01283042 , version 8 (12-01-2018)
hal-01283042 , version 9 (16-02-2018)
hal-01283042 , version 10 (29-05-2018)
hal-01283042 , version 11 (16-08-2018)
hal-01283042 , version 12 (18-10-2018)
hal-01283042 , version 13 (09-04-2019)
hal-01283042 , version 14 (14-04-2020)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

Petro Kolosov. Series Representation of Power Function. 2018. ⟨hal-01283042v9⟩
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