Multiply one Legendre series by another.
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.
c1, c2 : array_like
1-D arrays of Legendre series coefficients ordered from low to high.
out : ndarray
Of Legendre series coefficients representing their product.
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.
>>> from numpy.polynomial import legendre as L >>> c1 = (1,2,3) >>> c2 = (3,2) >>> P.legmul(c1,c2) # multiplication requires "reprojection" array([ 4.33333333, 10.4 , 11.66666667, 3.6 ])