(F, k, r, nu, **hints)
return InverseHankelTransform(F, k, r, nu).doit(**hints)
r"""
    Compute the inverse Hankel transform of `F` defined as

    .. math:: f(r) = \int_{0}^\infty F_\nu(k) J_\nu(k r) k \mathrm{d} k.

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`InverseHankelTransform` object.

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
    Note that for this transform, by default ``noconds=True``.

    >>> from sympy import hankel_transform, inverse_hankel_transform, gamma
    >>> from sympy import gamma, exp, sinh, cosh
    >>> from sympy.abc import r, k, m, nu, a

    >>> ht = hankel_transform(1/r**m, r, k, nu)
    >>> ht
    2*2**(-m)*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2)

    >>> inverse_hankel_transform(ht, k, r, nu)
    r**(-m)

    >>> ht = hankel_transform(exp(-a*r), r, k, 0)
    >>> ht
    a/(k**3*(a**2/k**2 + 1)**(3/2))

    >>> inverse_hankel_transform(ht, k, r, 0)
    exp(-a*r)

    See Also
    ========

    fourier_transform, inverse_fourier_transform
    sine_transform, inverse_sine_transform
    cosine_transform, inverse_cosine_transform
    hankel_transform
    mellin_transform, laplace_transform
r"""
    Compute the inverse Hankel transform of `F` defined as
r Compute the inverse Hankel transform of F defined as
def inverse_hankel_transform(F, k, r, nu, **hints):
    r"""
    Compute the inverse Hankel transform of `F` defined as

    .. math:: f(r) = \int_{0}^\infty F_\nu(k) J_\nu(k r) k \mathrm{d} k.

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`InverseHankelTransform` object.

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`.
    Note that for this transform, by default ``noconds=True``.

    >>> from sympy import hankel_transform, inverse_hankel_transform, gamma
    >>> from sympy import gamma, exp, sinh, cosh
    >>> from sympy.abc import r, k, m, nu, a

    >>> ht = hankel_transform(1/r**m, r, k, nu)
    >>> ht
    2*2**(-m)*k**(m - 2)*gamma(-m/2 + nu/2 + 1)/gamma(m/2 + nu/2)

    >>> inverse_hankel_transform(ht, k, r, nu)
    r**(-m)

    >>> ht = hankel_transform(exp(-a*r), r, k, 0)
    >>> ht
    a/(k**3*(a**2/k**2 + 1)**(3/2))

    >>> inverse_hankel_transform(ht, k, r, 0)
    exp(-a*r)

    See Also
    ========

    fourier_transform, inverse_fourier_transform
    sine_transform, inverse_sine_transform
    cosine_transform, inverse_cosine_transform
    hankel_transform
    mellin_transform, laplace_transform
    """
    return InverseHankelTransform(F, k, r, nu).doit(**hints)
def inverse_hankel_transform ( F , k , r , nu , * * hints ) : return InverseHankelTransform ( F , k , r , nu ) . doit ( * * hints )