Polynomials, power series and interpolation

Defining Power Series and Polynomials in Mizar

NONSYMMETRIC INTERPOLATION MACDONALD POLYNOMIALS AND gln BASIC HYPERGEOMETRIC SERIES

The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gln. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gln series.

Quantum Hermite Interpolation Polynomials

Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...

Stieltjes polynomials and Lagrange interpolation

Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...

Quantum interpolation of polynomials

Can a quantum computer efficiently interpolate polynomials? We consider blackbox algorithms that seek to learn information about a polynomial f from input/output pairs (xi, f(xi)). We define a more general class of (d, S)-independent function properties, where, outside of a set S of exceptions, knowing d input values does not help one predict the answer. There are essentially two strategies to ...