laguerre takes as argument an integer n and optionnally
a variable name (by default x) and a parameter name (by default a).
laguerre returns the Laguerre polynomial of degree n and of
parameter a.
If L(n,a,x) denotes the Laguerre polynomial of degree n and
parameter a, the following recurrence relation holds:
| L(0,a,x)=1, L(1,a,x)=1+a−x, L(n,a,x)= |
| L(n−1,a,x)− |
| L(n−2,a,x) |
These polynomials are orthogonal for the scalar product
| <f,g>= | ∫ |
| f(x)g(x)xae−xdx |
Input :
Output :
^2+-2*a*x+3*a+x^2+-4*x+2)/2Input :
Output :
^2+-2*a*y+3*a+y^2+-4*y+2)/2Input :
Output :
^2+-2*b*y+3*b+y^2+-4*y+2)/2