scipy.special.eval_laguerre

scipy.special.eval_laguerre(n, x, out=None) = <ufunc 'eval_laguerre'>

Evaluate Laguerre polynomial at a point.

The Laguerre polynomials can be defined via the confluent hypergeometric function \({}_1F_1\) as

\[L_n(x) = {}_1F_1(-n, 1, x).\]

See 22.5.16 and 22.5.54 in [AS] for details. When \(n\) is an integer the result is a polynomial of degree \(n\).

Parameters

narray_like

Degree of the polynomial. If not an integer the result is determined via the relation to the confluent hypergeometric function.

xarray_like

Points at which to evaluate the Laguerre polynomial

outndarray, optional

Optional output array for the function values

Returns

Lscalar or ndarray

Values of the Laguerre polynomial

See also

roots_laguerre

roots and quadrature weights of Laguerre polynomials

laguerre

Laguerre polynomial object

numpy.polynomial.laguerre.Laguerre

Laguerre series

eval_genlaguerre

evaluate generalized Laguerre polynomials

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.