numpy.polynomial.legendre.legmulx — NumPy v2.2 Manual (original) (raw)

polynomial.legendre.legmulx(c)[source]#

Multiply a Legendre series by x.

Multiply the Legendre series c by x, where x is the independent variable.

Parameters:

carray_like

1-D array of Legendre series coefficients ordered from low to high.

Returns:

outndarray

Array representing the result of the multiplication.

Notes

The multiplication uses the recursion relationship for Legendre polynomials in the form

\[xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1)\]

Examples

from numpy.polynomial import legendre as L L.legmulx([1,2,3]) array([ 0.66666667, 2.2, 1.33333333, 1.8]) # may vary