(f, t, s, **hints)
return LaplaceTransform(f, t, s).doit(**hints)
r"""
    Compute the Laplace Transform `F(s)` of `f(t)`,

    .. math :: F(s) = \int_0^\infty e^{-st} f(t) \mathrm{d}t.

    For all "sensible" functions, this converges absolutely in a
    half plane  `a < \operatorname{Re}(s)`.

    This function returns ``(F, a, cond)``
    where ``F`` is the Laplace transform of ``f``, `\operatorname{Re}(s) > a` is the half-plane
    of convergence, and ``cond`` are auxiliary convergence conditions.

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

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`. If ``noconds=True``,
    only `F` will be returned (i.e. not ``cond``, and also not the plane ``a``).

    >>> from sympy.integrals import laplace_transform
    >>> from sympy.abc import t, s, a
    >>> laplace_transform(t**a, t, s)
    (s**(-a)*gamma(a + 1)/s, 0, -re(a) < 1)

    See Also
    ========

    inverse_laplace_transform, mellin_transform, fourier_transform
    hankel_transform, inverse_hankel_transform
r"""
    Compute the Laplace Transform `F(s)` of `f(t)`,
r Compute the Laplace Transform F ( s ) of f ( t )
def laplace_transform(f, t, s, **hints):
    r"""
    Compute the Laplace Transform `F(s)` of `f(t)`,

    .. math :: F(s) = \int_0^\infty e^{-st} f(t) \mathrm{d}t.

    For all "sensible" functions, this converges absolutely in a
    half plane  `a < \operatorname{Re}(s)`.

    This function returns ``(F, a, cond)``
    where ``F`` is the Laplace transform of ``f``, `\operatorname{Re}(s) > a` is the half-plane
    of convergence, and ``cond`` are auxiliary convergence conditions.

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

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`. If ``noconds=True``,
    only `F` will be returned (i.e. not ``cond``, and also not the plane ``a``).

    >>> from sympy.integrals import laplace_transform
    >>> from sympy.abc import t, s, a
    >>> laplace_transform(t**a, t, s)
    (s**(-a)*gamma(a + 1)/s, 0, -re(a) < 1)

    See Also
    ========

    inverse_laplace_transform, mellin_transform, fourier_transform
    hankel_transform, inverse_hankel_transform
    """
    return LaplaceTransform(f, t, s).doit(**hints)
def laplace_transform ( f , t , s , * * hints ) : return LaplaceTransform ( f , t , s ) . doit ( * * hints )