منابع مشابه
h–analogue of Newton’s binomial formula
In this letter, the h–analogue of Newton’s binomial formula is obtained in the h–deformed quantum plane which does not have any q–analogue. For h = 0, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to n! (n−k)! for h = 1. Some properties of the h–binomial coefficients are also given. Finally, I hope that such results will contribute to an introduction ...
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In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [ x i ( xi ∂ ∂xi + (n− j)θ + u )]
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The q-binomial theorem is essentially the expansion of (x − 1)(x − q) · · · (x − q) in terms of the monomials x. In a recent paper [O], A. Okounkov has proved a beautiful multivariate generalization of this in the context of symmetric Macdonald polynomials [M1]. These polynomials have nonsymmetric counterparts [M2] which are of substantial interest, and in this paper we establish nonsymmetric a...
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The algebra I of polynomials in a single variable x provides a simple setting in which to do the "polynomial" calculus. Besides its being an algebra, one of the nicest features of I is that it is closed under both differentiation and antidifferentiation. That is to say, the derivative of a polynomial is another polynomial, and the antiderivative of a polynomial is another polynomial (provided w...
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Mahler's measure of a polynomial can be written as a logarithmic integral over the torus. We propose a deenition when the underlying group is an elliptic curve. Having reviewed some of the classical results in the toral case, we take some rst steps towards realising elliptic analogues. In particular, we focus on elliptic analogues of Kronecker's Theorem and Lehmer's problem. We wish to stress t...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/10/019