scipy.special.eval_sh_legendre — SciPy v1.15.2 Manual (original) (raw)

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

Evaluate shifted Legendre polynomial at a point.

These polynomials are defined as

\[P_n^*(x) = P_n(2x - 1)\]

where \(P_n\) is a Legendre polynomial. See 2.2.11 in [AS]for details.

Parameters:

narray_like

Degree of the polynomial. If not an integer, the value is determined via the relation to eval_legendre.

xarray_like

Points at which to evaluate the shifted Legendre polynomial

outndarray, optional

Optional output array for the function values

Returns:

Pscalar or ndarray

Values of the shifted Legendre polynomial

References

[AS]

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