numpy.polynomial.chebyshev.chebmul

numpy.polynomial.chebyshev.chebmul(c1, c2) [source]

Multiply one Chebyshev series by another.

Returns the product of two Chebyshev series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2.

Parameters

c1, c2array_like

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

Returns

outndarray

Of Chebyshev series coefficients representing their product.

See also

chebadd, chebsub, chebmulx, chebdiv, chebpow

Notes

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

Examples

>>> from numpy.polynomial import chebyshev as C
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> C.chebmul(c1,c2) # multiplication requires "reprojection"
array([  6.5,  12. ,  12. ,   4. ,   1.5])