# numpy.polynomial.laguerre.laggrid3d

polynomial.laguerre.laggrid3d(x, y, z, c)

  Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z.

  This function returns the values:

  \[p(a,b,c) = \sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c)\]

  where the points (a, b, c) consist of all triples formed by taking a from x, b from y, and c from z. The resulting points form a grid with x in the first dimension, y in the second, and z in the third.

  The parameters x, y, and z are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either x, y, and z or their elements must support multiplication and addition both with themselves and with the elements of c.

  If c has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape.

  Parameters
    x, y, z array_like, compatible objects

      The three dimensional series is evaluated at the points in the Cartesian product of x, y, and z. If x,`y`, or z is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn’t an ndarray, it is treated as a scalar.

    c array_like

      Array of coefficients ordered so that the coefficients for terms of degree i,j are contained in `c[i,j]`. If c has dimension greater than two the remaining indices enumerate multiple sets of coefficients.

  Returns
    values ndarray, compatible object

      The values of the two dimensional polynomial at points in the Cartesian product of x and y.

  See also

  `lagval`, `lagval2d`, `laggrid2d`, `lagval3d`

  Notes

  New in version 1.7.0.

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