`numpy.polynomial.legendre:legmul`

source: /numpy/polynomial/legendre.py:464

Signature

def legmul(c1, c2)

Summary

Multiply one Legendre series by another.

Extended Summary

Returns the product of two Legendre series c1 * c2. The arguments are sequences of coefficients, from lowest order "term" to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Parameters

c1, c2 : array_like: 1-D arrays of Legendre series coefficients ordered from low to high.

Returns

out : ndarray: Of Legendre series coefficients representing their product.

Notes

In general, the (polynomial) product of two C-series results in terms that are not in the Legendre polynomial basis set. Thus, to express the product as a Legendre series, it is necessary to "reproject" the product onto said basis set, which may produce "unintuitive" (but correct) results; see Examples section below.

Examples

from numpy.polynomial import legendre as L
c1 = (1,2,3)
c2 = (3,2)

✓

L.legmul(c1,c2) # multiplication requires "reprojection"

✗

array([ 4.3333, 10.4   , 11.6667,  3.6   ])

Aliases

numpy.polynomial.Legendre._mul
numpy.polynomial.legendre.legmul