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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:

<f,g>=
+∞


−∞
f(x)g(x)ex2dx 

The hermite command finds the Hermite polynomials.


Examples.


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