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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, 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.

  See also

  `legadd`, `legsub`, `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)
      >>> P.legmul(c1,c2) # multiplication requires "reprojection"
      array([  4.33333333,  10.4       ,  11.66666667,   3.6       ])

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