Email this article Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression
- Authors: Nikonov A.I1
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Affiliations:
- Samara State Technical University
- Issue: Vol 17, No 4 (2013)
- Pages: 184-191
- Section: Articles
- URL: https://journal-vniispk.ru/1991-8615/article/view/21064
- DOI: https://doi.org/10.14498/vsgtu1288
- ID: 21064
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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.
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##article.viewOnOriginalSite##About the authors
Alexander I Nikonov
Samara State Technical University
Email: nikonovai@mail.ru
(Dr. Techn. Sci.), Professor, Dept. of Electronic Systems and Information Security 244, Molodogvardeyskaya st., Samara, 443100, Russia
References
- А. И. Никонов, “Преобразование суммы взвешенных степеней натуральных чисел с одинаковыми показателями” // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2010. № 1(20). С. 258–262.
- А. И. Никонов, “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.
- А. И. Никонов, “Приведение суммы взвешенных одинаковых степеней к явному комбинаторному представлению” // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2012. № 3(28). С. 163–169.
- А. И. Никонов, Дискретная математика. Самара: СамГТУ, 2011. 106 с.
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