Abstract:
The correctness of equality which gives the combinatorial expression for the sum of the weighted equal powers of members of an arithmetical progression is found out. Such aspect provides usage of double summation of certain algebraic combinations with free and weight components of the given sum. Thus specified algebraic combinations also include binomial coefficients. Determination of required equality was made with use of comparison of real and hypothetical values.
Keywords:
sum of the weighted equal powers, real representation, hypothetical representation, binomial coefficients.
Original article submitted 10/X/2013 revision submitted – 12/XI/2013
Citation:
A. I. Nikonov, “Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(33) (2013), 184–191
\Bibitem{Nik13}
\by A.~I.~Nikonov
\paper Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 4(33)
\pages 184--191
\mathnet{http://mi.mathnet.ru/vsgtu1288}
\crossref{https://doi.org/10.14498/vsgtu1288}
\zmath{https://zbmath.org/?q=an:06968815}
\elib{https://elibrary.ru/item.asp?id=21159196}
Linking options:
https://www.mathnet.ru/eng/vsgtu1288
https://www.mathnet.ru/eng/vsgtu/v133/p184
This publication is cited in the following 1 articles:
A. I. Nikonov, “Ob odnom svoistve svobodnykh komponentov, otnosyaschikhsya k summam odinakovykh stepenei”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(36) (2014), 161–168
Citation in format AMSBIB
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