Laguerre polynomials: laguerre

### 2.26.3 Laguerre polynomials: `laguerre`

`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)= |
2n+a−1−x
n
| L(n−1,a,x)− |
n+a−1
n
| L(n−2,a,x)

These polynomials are orthogonal for the scalar product

<f,g>= | ∫ |
+∞
0
| f(x)g(x)xae−xdx

Input :

`laguerre(2)`

Output :

`(a```^```2+-2*a*x+3*a+x```^```2+-4*x+2)/2`

Input :

`laguerre(2,y)`

Output :

`(a```^```2+-2*a*y+3*a+y```^```2+-4*y+2)/2`

Input :

`laguerre(2,y,b)`

Output :

`(b```^```2+-2*b*y+3*b+y```^```2+-4*y+2)/2`