orthopoly
H
Hermite polynomial
Calling Sequence
Parameters
Description
Examples
H(n, x)
n
-
non-negative integer
x
algebraic expression
The H(n, x) function computes the nth Hermite polynomial evaluated at x.
The Hermite polynomials are orthogonal on the interval (−∞,∞) with respect to the weight function wx=ⅇ−x2. They satisfy:
∫−∞∞wtHn,tHm,tⅆt=0n≠mπ2nn!n=m
Hermite polynomials satisfy the following recurrence relation:
H0,x=1,
H1,x=2x,
Hn,x=2xHn−1,x−2n−1Hn−2,x,for n>1.
withorthopoly:
H2,x
4x2−2
H3,x
8x3−12x
H10,5
3275529760
See Also
HermiteH
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