Evaluate Laguerre polynomial
y=laguerre_eval(x,n)
a matrix of doubles
a 1-by-1 matrix of doubles, integer value, n>=0.
a matrix of doubles, the function value
Evaluates a Laguerre polynomial of degree n at point x.
The first Laguerre polynomials are
The remaining Laguerre polynomials satisfy the recurrence:
for n=1,2,....
x=linspace(0,10,100); y0=laguerre_eval(x,0); y1=laguerre_eval(x,1); y2=laguerre_eval(x,2); y3=laguerre_eval(x,3); h=scf(); plot(x,y0,"r-") plot(x,y1,"g-") plot(x,y2,"b-") plot(x,y3,"c:") xtitle("Laguerre Polynomials","x","He(x)") legend(["n=0","n=1","n=2","n=3"]); h.children.data_bounds(1:2,1)=[0;7]; h.children.data_bounds(1:2,2)=[-5;5]; h.children.children(4).children.thickness=3; h.children.children(5).children.thickness=2; h.children.children(5).children.line_style=5; | ![]() | ![]() |