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Orthogonal Polynomials >> Orthogonal Polynomials > Laguerre > laguerre_poly

laguerre_poly

Create Laguerre polynomial

Calling Sequence

y=laguerre_poly(n)

Parameters

n :

a 1-by-1 matrix of doubles, integer value, n>=0.

y :

a polynomial

Description

Create a Laguerre polynomial of degree n at point x.

The Laguerre polynomials are orthogonals with respect to the scalar product :

where w(x) is the Laguerre weight.

For n large (i.e.n>15), the evaluation of the polynomial with the horner function can be very inaccurate. To evaluate the polynomial, the laguerre_eval is more accurate.

Examples

y=laguerre_poly(0) // L0
y=laguerre_poly(1) // L1
y=laguerre_poly(2) // L2

for n=0:10
y=laguerre_poly(n);
disp(factorial(n)*y)
end

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