laguerre

laguerre (n, x)

The laguerre function returns the Laguerre polynomial of degree n (positive integer) and argument x. The polynomials satisfy the recurrence relation:

$$\displaystyle (n+1) \text { Laguerre }(n+1, x)=(2 n+1-x) \text { Laguerre }(n, x)-n \text { Laguerre }(n-1, x),$$

with the initial conditions

$$\displaystyle \text { Laguerre }(0, x)=1$$

and

$$\displaystyle \text { Laguerre }(1, x)=1-x .$$

See Also

laguerreA, laguerreGauss, chebyshev, chebyshevU, hermite, hermiteGauss, legendreA