1/23/13

Hermite polynomials

maxima maxima_hermite

Function: hermite( n, x )

Example:

    hermite(2,x);
    ratsimp(%);
    

Hermite Polynomial :

     H0(x) = 1 
     H1(x) = x 
     H2(x) = x^2 - 1
     H3(x) = x^3 - 3x
     H4(x) = x^4 - 6x^2 + 3
     H5(x) = x^5 - 10x^3 + 15x
      ... 
    

Recurrence Formurla :

     H_n+1(x) - x H_n(x) + n H_n-1(x) = 0
     H_n'(x) = n H_n-1(x)
    
See Also ...

maxima maxima_hermite