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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+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 

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

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