An iterative formula for the Kostka–Foulkes polynomials

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

An Explicit Formula for Lanczos Polynomials*

The Lanczos algorithm for tridiagonalizing a given matrix A generates a sequence of approximating matrices A, that can naturally be obtained as restrictions to subspaces. The eigenvalues of these approximating matrices are well known to be good approximations to the extreme eigenvalues of A. In this paper we produce explicit formulas for the characteristic polynomials of the A,, in terms of the...

An Explicit Formula for the Euler Product of Hecke Polynomials

An explicit formula is given for a sequence of numbers by using the Eichler-Selberg trace formula. A criterion is obtained by using these numbers for the location of nontrivial zeros of Hecke L-functions, which are associated with a family of cusp forms of weight 2.

An Analytic Formula for the A 2 Jack Polynomials ⋆

Abstract. In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451–482] on separation of variables (SoV) for the An Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27–34] where the integral representations for the A2 Jack polynomials was derived. Using special polynomial bases I shall obtain a more ...

The binomial formula for nonsymmetric Macdonald polynomials

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...