Laguerre polynomials

The Laguerre polynomial of degree n and parameter a satisfy the following recurrence relation:

L(0,a,x)

L(1,a,x)

=1+a−x

L(n,a,x)

2n+a−1−x

L(n−1,a,x)−

n+a−1

L(n−2,a,x)

These polynomials are orthogonal for the scalar product

⟨ f,g⟩=

∫

+∞

f(x)g(x)x^ae^−x dx.

The laguerre command finds the Laguerre polynomials.

laguerre takes one mandatory argument and two optional arguments:
- n, an integer.
- Optionally, x, a variable name (by default x).
- Optionally, a, a parameter name (by default a).
laguerre(n  ⟨,x,a⟩) returns the Laguerre polynomial of degree n and parameter a.

laguerre(2)

a²−a x+

x²−2 x+1

laguerre(2,y)

a²−a y+

y²−2 y+1

laguerre(2,y,b)

b²−b y+

y²−2 y+1