hermite takes as argument an integer n and
optionnally a variable name (by default x).
hermite returns the Hermite polynomial of degree n.
If H(n,x) denotes the Hermite polynomial of degree n,
the following recurrence relation holds:
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:
<f,g>= | ∫ |
| f(x)g(x)e−x2dx |
Input :
Output :
^
6+-480*x^
4+720*x^
2-120Input :
Output :
^
6+-480*y^
4+720*y^
2-120