(F, k, x, **hints)
return InverseCosineTransform(F, k, x).doit(**hints)
r"""
    Compute the unitary, ordinary-frequency inverse cosine transform of `F`,
    defined as

    .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \cos(2\pi x k) \mathrm{d} k.

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`InverseCosineTransform` 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 inverse_cosine_transform, exp, sqrt, pi
    >>> from sympy.abc import x, k, a
    >>> inverse_cosine_transform(sqrt(2)*a/(sqrt(pi)*(a**2 + k**2)), k, x)
    exp(-a*x)
    >>> inverse_cosine_transform(1/sqrt(k), k, x)
    1/sqrt(x)

    See Also
    ========

    fourier_transform, inverse_fourier_transform,
    sine_transform, inverse_sine_transform
    cosine_transform
    hankel_transform, inverse_hankel_transform
    mellin_transform, laplace_transform
r"""
    Compute the unitary, ordinary-frequency inverse cosine transform of `F`,
    defined as
r Compute the unitary ordinary - frequency inverse cosine transform of F defined as
def inverse_cosine_transform(F, k, x, **hints):
    r"""
    Compute the unitary, ordinary-frequency inverse cosine transform of `F`,
    defined as

    .. math:: f(x) = \sqrt{\frac{2}{\pi}} \int_{0}^\infty F(k) \cos(2\pi x k) \mathrm{d} k.

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`InverseCosineTransform` 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 inverse_cosine_transform, exp, sqrt, pi
    >>> from sympy.abc import x, k, a
    >>> inverse_cosine_transform(sqrt(2)*a/(sqrt(pi)*(a**2 + k**2)), k, x)
    exp(-a*x)
    >>> inverse_cosine_transform(1/sqrt(k), k, x)
    1/sqrt(x)

    See Also
    ========

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