# 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

Returns
Lndarray

Values of the generalized Laguerre polynomial

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.

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