scipy.special.eval_genlaguerre

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

Evaluate generalized Laguerre polynomial at a point.

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

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

When \(n\) is an integer the result is a polynomial of degree \(n\). See 22.5.54 in [AS] for details. The Laguerre polynomials are the special case where \(\alpha = 0\).

Parameters

narray_like

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

alphaarray_like

Parameter; must have alpha > -1

xarray_like

Points at which to evaluate the generalized Laguerre polynomial

outndarray, optional

Optional output array for the function values

Returns

Lscalar or ndarray

Values of the generalized Laguerre polynomial

See also

roots_genlaguerre

roots and quadrature weights of generalized Laguerre polynomials

genlaguerre

generalized Laguerre polynomial object

hyp1f1

confluent hypergeometric function

eval_laguerre

evaluate 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.