Hermite polynomial : hermite

### 4.26.2 Hermite polynomial : hermite

hermite takes as argument an integer n and optionally 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 :

hermite(6)

Output :

64*x`^`6+-480*x`^`4+720*x`^`2-120

Input :

hermite(6,y)

Output :

64*y`^`6+-480*y`^`4+720*y`^`2-120