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2.26.2  Hermite polynomial : hermite

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)ex2dx 

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

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