The coefficients of a Hermite polynomial

After the coomand:

H = hermiteH(n, sym('t')) ;

which generates a Hermite polynomial of degree n.

I need to get a vector of its coefficients.

Answer 1

[Paul]

coeffs

n = 4;
H = hermiteH(n, sym('t'))

H = 

[c,terms] = coeffs(H,sym('t'))

c = 

terms = 

or

[c,terms] = coeffs(H,sym('t'),'all')

c = 

terms = 

Typically one would declare t as workspace variable

syms t
H = hermiteH(n,t);
[c,terms] = coeffs(H,t,'all')

c = 

terms = 

Answer 2

[Matt J]

syms t
n = 4;                         % Degree of the Hermite polynomial
H = hermiteH(n, t);            % Generate Hermite polynomial of degree n
coeffs_vec = sym2poly(H);      % Get vector of coefficients
disp(coeffs_vec);

    16     0   -48     0    12

Answer 3

[David Goodmanson]

Hi Magdy,

For a change of pace, here is a function that calculates the coefficents of Hn by recursion. I didn't want to get into variable precision arithmetic but with double precision it's good to somewhere around n = 25. Usual Matlab notation so e.g.

hermite(6)
ans =  64     0  -480     0   720     0  -120        
means 64x^6 - 480x^4 + 720x^2 - 120 

function H = hermite(n)

% hermite polynomial coefficients
% usual Matlab convention with highest power first, constant term last
% H_n+1(x) = 2xH_n(x) - H_n(x)'
%
if n==0
  H = 1;
else
  A = hermite(n-1);
  H = 2*[A 0] - [0 0 (n-1:-1:1).*A(1:end-1)];
end