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6.30.3  Laguerre polynomials: laguerre

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

     
   L(0,a,x)=1         
L(1,a,x)=1+ax         
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)xaexdx 

The laguerre command finds the Laguerre polynomials.


Examples.


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