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numpy.polynomial.legendre.legmul

numpy.polynomial.legendre.legmul(c1, c2)

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.

Parameters

c1, c2array_like

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

Returns

outndarray

Of Legendre series coefficients representing their product.

See also

legadd, legsub, legmulx, legdiv, legpow

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([  4.33333333,  10.4       ,  11.66666667,   3.6       ]) # may vary