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File Content: `_spherical_bessel.cpython-35.pyc`



DB�Wd������������������@���s����d��d�l��m�Z�m�Z�m�Z�d�d�l�m�Z�m�Z�m�Z�m�Z�m	�Z	�m
�Z
�m�Z�m�Z�d�d�d���Z
�d�d�d���Z�d�d	�d
���Z�d�d�d���Z�d
�S)�����)�division�print_function�absolute_import����)�
_spherical_jn�
_spherical_yn�
_spherical_in�
_spherical_kn�_spherical_jn_d�_spherical_yn_d�_spherical_in_d�_spherical_kn_dFc�������������C���s$���|�r�t��|��|���St�|��|���Sd�S)a���Spherical Bessel function of the first kind or its derivative.

    Defined as [1]_,

    .. math:: j_n(z) = \sqrt{\frac{\pi}{2z}} J_{n + 1/2}(z),

    where :math:`J_n` is the Bessel function of the first kind.

    Parameters
    ----------
    n : int, array_like
        Order of the Bessel function (n >= 0).
    z : complex or float, array_like
        Argument of the Bessel function.
    derivative : bool, optional
        If True, the value of the derivative (rather than the function
        itself) is returned.

    Returns
    -------
    jn : ndarray

    Notes
    -----
    For real arguments greater than the order, the function is computed
    using the ascending recurrence [2]_.  For small real or complex
    arguments, the definitional relation to the cylindrical Bessel function
    of the first kind is used.

    The derivative is computed using the relations [3]_,

    .. math::
        j_n' = j_{n-1} - \frac{n + 1}{2} j_n.

        j_0' = -j_1


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] http://dlmf.nist.gov/10.47.E3
    .. [2] http://dlmf.nist.gov/10.51.E1
    .. [3] http://dlmf.nist.gov/10.51.E2
    N)r
���r���)�n�z�
derivative��r����/_spherical_bessel.py�spherical_jn���s����.
r���c�������������C���s$���|�r�t��|��|���St�|��|���Sd�S)ae��Spherical Bessel function of the second kind or its derivative.

    Defined as [1]_,

    .. math:: y_n(z) = \sqrt{\frac{\pi}{2z}} Y_{n + 1/2}(z),

    where :math:`Y_n` is the Bessel function of the second kind.

    Parameters
    ----------
    n : int, array_like
        Order of the Bessel function (n >= 0).
    z : complex or float, array_like
        Argument of the Bessel function.
    derivative : bool, optional
        If True, the value of the derivative (rather than the function
        itself) is returned.

    Returns
    -------
    yn : ndarray

    Notes
    -----
    For real arguments, the function is computed using the ascending
    recurrence [2]_.  For complex arguments, the definitional relation to
    the cylindrical Bessel function of the second kind is used.

    The derivative is computed using the relations [3]_,

    .. math::
        y_n' = y_{n-1} - \frac{n + 1}{2} y_n.

        y_0' = -y_1


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] http://dlmf.nist.gov/10.47.E4
    .. [2] http://dlmf.nist.gov/10.51.E1
    .. [3] http://dlmf.nist.gov/10.51.E2
    N)r���r���)r���r���r���r���r���r����spherical_yn;���s����-
r���c�������������C���s$���|�r�t��|��|���St�|��|���Sd�S)a���Modified spherical Bessel function of the first kind or its derivative.

    Defined as [1]_,

    .. math:: i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),

    where :math:`I_n` is the modified Bessel function of the first kind.

    Parameters
    ----------
    n : int, array_like
        Order of the Bessel function (n >= 0).
    z : complex or float, array_like
        Argument of the Bessel function.
    derivative : bool, optional
        If True, the value of the derivative (rather than the function
        itself) is returned.

    Returns
    -------
    in : ndarray

    Notes
    -----
    The function is computed using its definitional relation to the
    modified cylindrical Bessel function of the first kind.

    The derivative is computed using the relations [2]_,

    .. math::
        i_n' = i_{n-1} - \frac{n + 1}{2} i_n.

        i_1' = i_0


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] http://dlmf.nist.gov/10.47.E7
    .. [2] http://dlmf.nist.gov/10.51.E5
    N)r���r���)r���r���r���r���r���r����spherical_inn���s����+
r���c�������������C���s$���|�r�t��|��|���St�|��|���Sd�S)a��Modified spherical Bessel function of the second kind or its derivative.

    Defined as [1]_,

    .. math:: k_n(z) = \sqrt{\frac{\pi}{2z}} K_{n + 1/2}(z),

    where :math:`K_n` is the modified Bessel function of the second kind.

    Parameters
    ----------
    n : int, array_like
        Order of the Bessel function (n >= 0).
    z : complex or float, array_like
        Argument of the Bessel function.
    derivative : bool, optional
        If True, the value of the derivative (rather than the function
        itself) is returned.

    Returns
    -------
    kn : ndarray

    Notes
    -----
    The function is computed using its definitional relation to the
    modified cylindrical Bessel function of the second kind.

    The derivative is computed using the relations [2]_,

    .. math::
        k_n' = -k_{n-1} - \frac{n + 1}{2} k_n.

        k_0' = -k_1


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] http://dlmf.nist.gov/10.47.E9
    .. [2] http://dlmf.nist.gov/10.51.E5
    N)r
���r	���)r���r���r���r���r���r����spherical_kn����s����+
r���N)Z
__future__r���r���r���Z_ufuncsr���r���r���r	���r
���r���r���r
���r���r���r���r���r���r���r���r����<module>���s
���:431

Name	Size	Permission
__init__.cpython-35.opt-1.pyc	23337 bytes	0644
__init__.cpython-35.pyc	23337 bytes	0644
_ellip_harm.cpython-35.opt-1.pyc	5949 bytes	0644
_ellip_harm.cpython-35.pyc	5949 bytes	0644
_mptestutils.cpython-35.opt-1.pyc	13427 bytes	0644
_mptestutils.cpython-35.pyc	13427 bytes	0644
_spherical_bessel.cpython-35.opt-1.pyc	5467 bytes	0644
_spherical_bessel.cpython-35.pyc	5467 bytes	0644
_testutils.cpython-35.opt-1.pyc	10670 bytes	0644
_testutils.cpython-35.pyc	10670 bytes	0644
add_newdocs.cpython-35.opt-1.pyc	132479 bytes	0644
add_newdocs.cpython-35.pyc	132479 bytes	0644
basic.cpython-35.opt-1.pyc	72955 bytes	0644
basic.cpython-35.pyc	72955 bytes	0644
generate_ufuncs.cpython-35.opt-1.pyc	41799 bytes	0644
generate_ufuncs.cpython-35.pyc	41799 bytes	0644
lambertw.cpython-35.opt-1.pyc	3191 bytes	0644
lambertw.cpython-35.pyc	3191 bytes	0644
orthogonal.cpython-35.opt-1.pyc	54319 bytes	0644
orthogonal.cpython-35.pyc	54319 bytes	0644
setup.cpython-35.opt-1.pyc	3206 bytes	0644
setup.cpython-35.pyc	3206 bytes	0644
spfun_stats.cpython-35.opt-1.pyc	2299 bytes	0644
spfun_stats.cpython-35.pyc	2299 bytes	0644

File Content: _spherical_bessel.cpython-35.pyc

File Content: `_spherical_bessel.cpython-35.pyc`