6.30.2 Hermite polynomial: hermite
The Hermite polynomials H(n,x) satisfy the recurrence relation:
| H(0,x) | =1 | | | | | | | | | |
H(1,x) | =2x | | | | | | | | | |
H(n,x)=2xH(n−1,x)−2(n−1)H(n−2,x)
| | | | | | | | | | |
|
These polynomials are orthogonal for the scalar product:
The hermite command finds the Hermite polynomials.
-
hermite takes one mandatory argument and one
optional argument:
-
n, an integer.
- Optionally, x, a variable name (by default
x).
- hermite(n ⟨ ,x⟩)
returns the Hermite polynomial of degree n.
Examples.
-
Input:
hermite(6)
Output:
- Input:
hermite(6,y)
Output: