REPRESENTATION OF SOME BINOMIAL COEFFICIENTS BY POLYNOMIALS

Title & Authors
REPRESENTATION OF SOME BINOMIAL COEFFICIENTS BY POLYNOMIALS
Kim, Seon-Hong;

Abstract
The unique positive zero of $\small{F_m(z):=z^{2m}-z^{m+1}-z^{m-1}-1}$ leads to analogues of $\small{2(\array{2n\\k}\)}$(k even) by using hypergeometric functions. The minimal polynomials of these analogues are related to Chebyshev polynomials, and the minimal polynomial of an analogue of $\small{2(\array{2n\\k}\)}$(k even>2) can be computed by using an analogue of $\small{2(\array{2n\\k}\)}$. In this paper we show that the analogue of $\small{2(\array{2n\\2}\)}$. In this paper we show that the analygue $\small{2(\array{2n\\2}\)}$ is the only real zero of its minimal polynomial, and has a different representation, by using a polynomial of smaller degree than $\small{F_m}$(z).
Keywords
binomial coefficients;analogues;minimal polynomial;Chebyshev polynomial;
Language
English
Cited by
References
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