Function hermemulx

numpy/polynomial/hermite_e.py:392–438

Multiply a Hermite series by x. Multiply the Hermite series `c` by x, where x is the independent variable. Parameters ---------- c : array_like 1-D array of Hermite series coefficients ordered from low to high. Returns ------- out : ndarray

(c)

def hermemulx(c):
    """Multiply a Hermite series by x.

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


    Parameters
    ----------
    c : array_like
        1-D array of Hermite series coefficients ordered from low to
        high.

    Returns
    -------
    out : ndarray
        Array representing the result of the multiplication.

    Notes
    -----
    The multiplication uses the recursion relationship for Hermite
    polynomials in the form

    .. math::

        xP_i(x) = (P_{i + 1}(x) + iP_{i - 1}(x)))

    Examples
    --------
    >>> from numpy.polynomial.hermite_e import hermemulx
    >>> hermemulx([1, 2, 3])
    array([2.,  7.,  2.,  3.])

    """
    # c is a trimmed copy
    [c] = pu.as_series([c])
    # The zero series needs special treatment
    if len(c) == 1 and c[0] == 0:
        return c

    prd = np.empty(len(c) + 1, dtype=c.dtype)
    prd[0] = c[0]*0
    prd[1] = c[0]
    for i in range(1, len(c)):
        prd[i + 1] = c[i]
        prd[i - 1] += c[i]*i
    return prd


def hermemul(c1, c2):