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Representation of some binomial coefficients by polynomials

Authors
Kim, Seon-Hong
Issue Date
Nov-2007
Publisher
KOREAN MATHEMATICAL SOC
Keywords
binomial coefficients; analogues; minimal polynomial; Chebyshev polynomial
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.44, no.4, pp.677 - 682
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
44
Number
4
Start Page
677
End Page
682
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/14619
DOI
10.4134/BKMS.2007.44.4.677
ISSN
1015-8634
Abstract
The unique Positive zero of F-m (z) := z(2m) - z(m+1) - z(m-1) - 1 leads to analogues of 2 ((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 2((2n)(k)) (k even > 2) can be computed by using an analogue of 2 ((2n)(2)). In this paper we show that the analogue of 2((2n)(2)) is the only real zero of its minimal polynomial, and has a different representation, by using a polynomial of smaller degree than F-m (z).
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