Campus Livre
hermiteH
Hermite polynomial.
Category: Mathematics > Polynomials
Syntax
P = hermiteH(n, x)Evaluates the Hermite polynomial of degree n at x.
Description
H_n(x) is the physicists' Hermite polynomial, orthogonal on the whole real line with weight exp(-x^2). It satisfies H_(n+1) = 2*x*H_n - 2*n*H_(n-1) with H_0 = 1 and H_1 = 2*x.
These polynomials give the wave functions of the quantum harmonic oscillator. The probabilists' version, with weight exp(-x^2/2), is a rescaled form of the same family.
Input arguments
n- Degree, a nonnegative integer or a symbolic variable.
x- Point(s) of evaluation, or a symbolic variable to get the polynomial.
Output arguments
P- Numbers with the size of
x, or a symbolic polynomial.
Example
Polynomials and a value
syms x
hermiteH(2:4, x)
hermiteH(3, 2)Output
ans =
[4*x^2 - 2, 8*x^3 - 12*x, 16*x^4 - 48*x^2 + 12]
ans = 40