(F, s, t, plane=None, **hints)
return InverseLaplaceTransform(F, s, t, plane).doit(**hints)
r"""
    Compute the inverse Laplace transform of `F(s)`, defined as

    .. math :: f(t) = \int_{c-i\infty}^{c+i\infty} e^{st} F(s) \mathrm{d}s,

    for `c` so large that `F(s)` has no singularites in the
    half-plane `\operatorname{Re}(s) > c-\epsilon`.

    The plane can be specified by
    argument ``plane``, but will be inferred if passed as None.

    Under certain regularity conditions, this recovers `f(t)` from its
    Laplace Transform `F(s)`, for non-negative `t`, and vice
    versa.

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

    Note that this function will always assume `t` to be real,
    regardless of the sympy assumption on `t`.

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`.

    >>> from sympy.integrals.transforms import inverse_laplace_transform
    >>> from sympy import exp, Symbol
    >>> from sympy.abc import s, t
    >>> a = Symbol('a', positive=True)
    >>> inverse_laplace_transform(exp(-a*s)/s, s, t)
    Heaviside(-a + t)

    See Also
    ========

    laplace_transform
    hankel_transform, inverse_hankel_transform
r"""
    Compute the inverse Laplace transform of `F(s)`, defined as
r Compute the inverse Laplace transform of F ( s ) defined as
def inverse_laplace_transform(F, s, t, plane=None, **hints):
    r"""
    Compute the inverse Laplace transform of `F(s)`, defined as

    .. math :: f(t) = \int_{c-i\infty}^{c+i\infty} e^{st} F(s) \mathrm{d}s,

    for `c` so large that `F(s)` has no singularites in the
    half-plane `\operatorname{Re}(s) > c-\epsilon`.

    The plane can be specified by
    argument ``plane``, but will be inferred if passed as None.

    Under certain regularity conditions, this recovers `f(t)` from its
    Laplace Transform `F(s)`, for non-negative `t`, and vice
    versa.

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

    Note that this function will always assume `t` to be real,
    regardless of the sympy assumption on `t`.

    For a description of possible hints, refer to the docstring of
    :func:`sympy.integrals.transforms.IntegralTransform.doit`.

    >>> from sympy.integrals.transforms import inverse_laplace_transform
    >>> from sympy import exp, Symbol
    >>> from sympy.abc import s, t
    >>> a = Symbol('a', positive=True)
    >>> inverse_laplace_transform(exp(-a*s)/s, s, t)
    Heaviside(-a + t)

    See Also
    ========

    laplace_transform
    hankel_transform, inverse_hankel_transform
    """
    return InverseLaplaceTransform(F, s, t, plane).doit(**hints)
def inverse_laplace_transform ( F , s , t , plane = None , * * hints ) : return InverseLaplaceTransform ( F , s , t , plane ) . doit ( * * hints )