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

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

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`CosineTransform` 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 cosine_transform, exp, sqrt, cos
    >>> from sympy.abc import x, k, a
    >>> cosine_transform(exp(-a*x), x, k)
    sqrt(2)*a/(sqrt(pi)*(a**2 + k**2))
    >>> cosine_transform(exp(-a*sqrt(x))*cos(a*sqrt(x)), x, k)
    a*exp(-a**2/(2*k))/(2*k**(3/2))

    See Also
    ========

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

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

    If the transform cannot be computed in closed form, this
    function returns an unevaluated :class:`CosineTransform` 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 cosine_transform, exp, sqrt, cos
    >>> from sympy.abc import x, k, a
    >>> cosine_transform(exp(-a*x), x, k)
    sqrt(2)*a/(sqrt(pi)*(a**2 + k**2))
    >>> cosine_transform(exp(-a*sqrt(x))*cos(a*sqrt(x)), x, k)
    a*exp(-a**2/(2*k))/(2*k**(3/2))

    See Also
    ========

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