numpy.polynomial.legendre.legmulx

polynomial.legendre.legmulx(c) [source]

Multiply a Legendre series by x.

Multiply the Legendre series c by x, where x is the independent variable.

Parameters

carray_like

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

Returns

outndarray

Array representing the result of the multiplication.

See also

legadd, legmul, legmul, legdiv, legpow

Notes

The multiplication uses the recursion relationship for Legendre polynomials in the form

\[xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1)\]

Examples

>>> from numpy.polynomial import legendre as L
>>> L.legmulx([1,2,3])
array([ 0.66666667, 2.2, 1.33333333, 1.8]) # may vary