Representation of some binomial coefficients by polynomials

초록

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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