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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) = $\displaystyle {\frac{{2n+a-1-x}}{{n}}}$L(n - 1, a, x) - $\displaystyle {\frac{{n+a-1}}{{n}}}$L(n - 2, a, x)

These polynomials are orthogonal for the scalar product

< f, g > = $\displaystyle \int_{{0}}^{{+\infty}}$f (x)g(x)xae-xdx

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giac documentation written by Renée De Graeve and Bernard Parisse