Geodesic
The update exposition of the components organising the sum of weighted equal powers
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 223-232.

Voir la notice de l'article provenant de la source Math-Net.Ru

The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients. Modification of components of the first aspect uses explicitly expressed products of binomial coefficients, and modification of components of the second aspect - products of binomial and weight coefficients. These visible expressions expand possibilities of representation of structure and an order of shaping of the considered sums.
Keywords: sum of the weighted equal powers, binomial and weight coefficients, product of binomial and weight coefficients, update expressions.
Mots-clés : product of binomial coefficients 
@article{VSGTU_2012_1_a23,
     author = {A. I. Nikonov},
     title = {The update exposition of the components organising the sum of weighted equal powers},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {223--232},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a23/}
}
TY  - JOUR
AU  - A. I. Nikonov
TI  - The update exposition of the components organising the sum of weighted equal powers
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2012
SP  - 223
EP  - 232
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a23/
LA  - ru
ID  - VSGTU_2012_1_a23
ER  - 
%0 Journal Article
%A A. I. Nikonov
%T The update exposition of the components organising the sum of weighted equal powers
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2012
%P 223-232
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a23/
%G ru
%F VSGTU_2012_1_a23
A. I. Nikonov. The update exposition of the components organising the sum of weighted equal powers. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 223-232. http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a23/

[1] Nikonov A. I., “Converting the sum of weighted degrees of natural numbers with the same parameters”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 1(20), 258–262 | DOI

[2] Nikonov A. I., “On one property of the weighed sums of equal powers as matrix products”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 5(21), 313–317 | DOI

[3] Nikonov A. I., “Matrix representation of the sum of the weighted equal powers with natural base numbers”, Matematics. Computing. Education: Collect. of scient. abstracts 18th International Conf, Pushchino, 2011, 123

[4] Anderson J. A., Discrete Mathematics with Combinatorics, 2nd Edn, Prentice Hall, Upper Saddle River, NJ, 2003, 928 pp.; Anderson Dzh., Diskretnaya matematika i kombinatorika, Vilyams, M., 2004, 960 pp.

[5] Vilenkin N. Ya., Combinatorics, Nauka, Moscow, 1969, 328 pp. | MR | Zbl

[6] Turner J. C., Modern applied mathematics: probability, statistics, operational research, English Universities Press, London, 1970, 502 pp.; Terner D., Veroyatnost, statistika i issledovanie operatsii, Statistika, M., 1976, 432 pp.