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.