Lucas Polynomials and Power Sums

被引:0
作者
Tamm, Ulrich [1 ]
机构
[1] Marmara Univ Istanbul, Dept Business Informat, Istanbul, Turkey
来源
2013 INFORMATION THEORY AND APPLICATIONS WORKSHOP (ITA) | 2013年
关键词
orthogonal polynomials; Chebyshev polynomials; Lucas polynomials; Girard - Waring formula; zeta function;
D O I
暂无
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The three - term recurrence x(n) + y(n) = (x + y) . (x(n-1) + y(n-1)) - xy . (x(n-2) + y(n-2)) allows to express x(n) + y(n) as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be. It can be explained algebraically via the Girard - Waring formula, combinatorially via Lucas numbers and polynomials, and analytically as a special orthogonal polynomial. We shall briefly describe all these aspects and present an application from number theory.
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页数:4
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