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.