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REPRESENTATION OF SOME BINOMIAL COEFFICIENTS BY POLYNOMIALS
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 Title & Authors
REPRESENTATION OF SOME BINOMIAL COEFFICIENTS BY POLYNOMIALS
Kim, Seon-Hong;
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 Abstract
The unique positive zero of leads to analogues of (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 (k even>2) can be computed by using an analogue of . In this paper we show that the analogue of . In this paper we show that the analygue is the only real zero of its minimal polynomial, and has a different representation, by using a polynomial of smaller degree than (z).
 Keywords
binomial coefficients;analogues;minimal polynomial;Chebyshev polynomial;
 Language
English
 Cited by
 References
1.
S.-H. Kim, Factorization of sums of polynomials, Acta Appl. Math. 73 (2002), no. 3, 275-284 crossref(new window)

2.
S.-H. Kim, The analogues of some binomial coefficients, Indian J. Pure Appl. Math. 34 (2003), no. 12, 1771-1784

3.
T. Kim, H. K. Pak, C. S. Ryoo, S. H. Rim, and L. C. Jang, Introduction to q-Number Theory, Kyo Woo Sa, Seoul, 2006

4.
M. Marden, Geometry of Polynomials, Second edition, Mathematical Surveys, No. 3 American Mathematical Society, Providence, R.I., 1966