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Module « scipy.special »

Fonction sph_harm - module scipy.special

Signature de la fonction sph_harm

def sph_harm(*args, **kwargs) 

Description

help(scipy.special.sph_harm)

sph_harm(x1, x2, x3, x4, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    sph_harm(m, n, theta, phi, out=None)

    Compute spherical harmonics.

    The spherical harmonics are defined as

    .. math::

        Y^m_n(\theta,\phi) = \sqrt{\frac{2n+1}{4\pi} \frac{(n-m)!}{(n+m)!}}
          e^{i m \theta} P^m_n(\cos(\phi))

    where :math:`P_n^m` are the associated Legendre functions; see `lpmv`.

    .. deprecated:: 1.15.0
        This function is deprecated and will be removed in SciPy 1.17.0.
        Please use `scipy.special.sph_harm_y` instead.

    Parameters
    ----------
    m : array_like
        Order of the harmonic (int); must have ``|m| <= n``.
    n : array_like
       Degree of the harmonic (int); must have ``n >= 0``. This is
       often denoted by ``l`` (lower case L) in descriptions of
       spherical harmonics.
    theta : array_like
       Azimuthal (longitudinal) coordinate; must be in ``[0, 2*pi]``.
    phi : array_like
       Polar (colatitudinal) coordinate; must be in ``[0, pi]``.
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    y_mn : complex scalar or ndarray
       The harmonic :math:`Y^m_n` sampled at ``theta`` and ``phi``.

    Notes
    -----
    There are different conventions for the meanings of the input
    arguments ``theta`` and ``phi``. In SciPy ``theta`` is the
    azimuthal angle and ``phi`` is the polar angle. It is common to
    see the opposite convention, that is, ``theta`` as the polar angle
    and ``phi`` as the azimuthal angle.

    Note that SciPy's spherical harmonics include the Condon-Shortley
    phase [2]_ because it is part of `lpmv`.

    With SciPy's conventions, the first several spherical harmonics
    are

    .. math::

        Y_0^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{1}{\pi}} \\
        Y_1^{-1}(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{2\pi}}
                                    e^{-i\theta} \sin(\phi) \\
        Y_1^0(\theta, \phi) &= \frac{1}{2} \sqrt{\frac{3}{\pi}}
                                 \cos(\phi) \\
        Y_1^1(\theta, \phi) &= -\frac{1}{2} \sqrt{\frac{3}{2\pi}}
                                 e^{i\theta} \sin(\phi).

    References
    ----------
    .. [1] Digital Library of Mathematical Functions, 14.30.
           https://dlmf.nist.gov/14.30
    .. [2] https://en.wikipedia.org/wiki/Spherical_harmonics#Condon.E2.80.93Shortley_phase
    

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