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legmul(c1, c2)

Returns the product of two Legendre series :None:None:`c1` * :None:None:`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 .

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.

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.

Multiply one Legendre series by another.

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

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.polynomial.legendre.legsub numpy.polynomial.legendre.legmulx numpy.polynomial.legendre.legadd numpy.polynomial.legendre.legpow numpy.polynomial.legendre.legdiv

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