Email this article Reduction of the sum of the weighted equal powers to explicit combinatorial representation
- Authors: Nikonov A.I1
-
Affiliations:
- Samara State Technical University
- Issue: Vol 16, No 3 (2012)
- Pages: 163-169
- Section: Articles
- URL: https://bakhtiniada.ru/1991-8615/article/view/20867
- ID: 20867
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Abstract
The paper contains the proof of the statement that the component of the sum of weighted powers with natural bases and equal parameters, dependent on weight coefficients, is equal to the sum of products of binomial and weight coefficients. It is proved also, that the component of this sum, independent of weight coefficients, is the algebraic sum of products of binomial coefficients and powers of natural numbers. Explicit combinatorial representation of the sum of the weighted equal powers contains the magnitudes taken from proved equalities.
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##article.viewOnOriginalSite##About the authors
Alexander I Nikonov
Samara State Technical University
Email: nikonovai@mail.ru
(Dr. Sci. (Tech.)), Professor, Dept. of Electronic Systems and Information Security 244, Molodogvardeyskaya st., Samara, 443100, Russia
References
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- Никонов А. И. Об одном свойстве взвешенных сумм одинаковых степеней как матричных произведений // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2010. № 5(21). С. 313–317.
- Никонов А. И. Модифицированное описание компонентов, образующих сумму взвешенных одинаковых степеней // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2012. № 1(26). С. 223–232.
- Виленкин Н. Я. Комбинаторика. М.: Наука, 1969. 328 с.
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