Hermite Polynomial -- octave_polynomial_Hermite.m

octave_polynomial_Hermite

Function: H = octave_polynomial_Hermite ( n )

Example:

octave:> H = octave_polynomial_Hermite( 5 )
H = 
     1    0  -10    0   15    0

octave_polynomial_Hermite.m File:

function H0 = octave_polynomial_Hermite( n )

 H0 = [1];
 H1 = [1,0];
 for i=1:n
  H0_1 = i * H0;
  H0_2 = conv ( [0,0,1], H0_1 );

  H2 = conv( [1,0], H1 ) - H0_2;
  
  H0 = H1;
  H1 = H2;
 end

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)
 

octave_polynomial_Hermite.m

octave_polynomial_Hermite