# Hermite(n,x) polynomials; # Hermite(n) number; #hermite(0):= 1; #hermite(1):= 0; #hermite(n_,x_):=if(n>0, expand(2x*hermite(n-1,x)-2*(n-1)*hermite(n-2,x)), if(n< -1, exp(x^2/2)*expand(2x*hermite(-n-2,x)+2*(-n-2)*hermite(-n-3,x)) )); #hermite(2,x_):= 4x^2-2; #hermite(3,x_):= 8x^3-12x; #hermite(4,x_):= 16x^4-48x^2+12; #hermite(5,x_):= 32x^5-160x^3+120x; #hermite(6,x_):= 64x^6-480x^4+720x^2-120; #hermite(7,x_):= 128x^7-1344x^5+3360x^3-1680x; #hermite(8,x_):= 256x^8-3584x^6+13440x^4-13440x^2+1680; #hermite(9,x_):= 512x^9-9216x^7+48384x^5-80640x^3+30240x; #hermite(10,x_):=1024x^(10)-23040x^8+161280x^6-403200x^4+302400x^2-30240; #hermite(n_,x_):=if(n>0, expand(2x*hermite(n-1,x)-2*(n-1)*hermite(n-2,x)), if(n<0, expand(2x*hermite(n+1,x)-2*(n+1)*hermite(n+2,x)) )); hermite(-1,x_):=sqrt(pi)/2*exp(x^2)*erfc(x); hermite(0,x_):=1; hermite(1,x_):= 2x; hermite(n_):=if(isodd(n),0, hermite(n,0) );