We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested.

In this article we investigate the minimal dimension of a subspace of C1(R2) needed to interpolate an arbitrary function and some of its prescribed partial derivatives at two arbitrary points. The subspace in question may depend on the derivatives, but not on the location of the points. Several results of this type are known for Lagrange interpolation. As far as I know, this is the first such s...

Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily distributed points in C. (N + M) work, ...

The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schrödinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted t...

One of the most interesting proofs is due to Hermite; it arose as a byproduct of his proof of the transcendence of e in [5]. (See [6] for an exposition by Olds.) The purpose of this note is to present an especially short and direct variant of Hermite’s proof and to explain some of the motivation behind it. Consider any continued fraction [a0, a1, a2, . . .]. Its ith convergent is defined to be ...

Steerability is a useful and important property of “kernel” functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high e±ciency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by theGaussian functionwith di®erent powers, de ̄ned as the Hermite kernel. Certain special cases of suc...