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# sympy.integrals.meijerint.meijerint_inversion

All Samples(12)  |  Call(8)  |  Derive(0)  |  Import(4)

```def _inverse_laplace_transform(F, s, t_, plane, simplify=True):
""" The backend function for inverse Laplace transforms. """
from sympy import exp, Heaviside, log, expand_complex, Integral, Piecewise
from sympy.integrals.meijerint import meijerint_inversion, _get_coeff_exp
# There are two strategies we can try:
```
```        f = None
if f is None:
f = meijerint_inversion(F, s, t)
if f is None:
raise IntegralTransformError('Inverse Laplace', f, '')
```

```def _inverse_laplace_transform(F, s, t_, plane, simplify=True):
""" The backend function for inverse Laplace transforms. """
from sympy import exp, Heaviside, log, expand_complex, Integral, Piecewise
from sympy.integrals.meijerint import meijerint_inversion, _get_coeff_exp
# There are two strategies we can try:
```
```        f = None
if f is None:
f = meijerint_inversion(F, s, t)
if f is None:
raise IntegralTransformError('Inverse Laplace', f, '')
```

```from sympy import (meijerg, I, S, integrate, Integral, oo, gamma,
hyperexpand, exp, simplify, sqrt, pi, erf, sin, cos,
exp_polar, polar_lift, polygamma, hyper, log, expand_func)
from sympy.integrals.meijerint import (_rewrite_single, _rewrite1,
meijerint_indefinite, _inflate_g, _create_lookup_table,
```
```    def inv(f):
return piecewise_fold(meijerint_inversion(f, s, t))
assert inv(1/(s**2 + 1)) == sin(t)*Heaviside(t)
assert inv(s/(s**2 + 1)) == cos(t)*Heaviside(t)
assert inv(exp(-s)/s) == Heaviside(t - 1)
assert inv(1/sqrt(1 + s**2)) == besselj(0, t)*Heaviside(t)

# Test some antcedents checking.
assert meijerint_inversion(sqrt(s)/sqrt(1 + s**2), s, t) is None
```
```    assert meijerint_inversion(sqrt(s)/sqrt(1 + s**2), s, t) is None
assert inv(exp(s**2)) is None
assert meijerint_inversion(exp(-s**2), s, t) is None

```

```from sympy import (meijerg, I, S, integrate, Integral, oo, gamma,
hyperexpand, exp, simplify, sqrt, pi, erf, sin, cos,
exp_polar, polar_lift, polygamma, hyper, log, expand_func)
from sympy.integrals.meijerint import (_rewrite_single, _rewrite1,
meijerint_indefinite, _inflate_g, _create_lookup_table,
```
```    def inv(f):
return piecewise_fold(meijerint_inversion(f, s, t))
assert inv(1/(s**2 + 1)) == sin(t)*Heaviside(t)
assert inv(s/(s**2 + 1)) == cos(t)*Heaviside(t)
assert inv(exp(-s)/s) == Heaviside(t - 1)
assert inv(1/sqrt(1 + s**2)) == besselj(0, t)*Heaviside(t)

# Test some antcedents checking.
assert meijerint_inversion(sqrt(s)/sqrt(1 + s**2), s, t) is None
```
```    assert meijerint_inversion(sqrt(s)/sqrt(1 + s**2), s, t) is None
assert inv(exp(s**2)) is None
assert meijerint_inversion(exp(-s**2), s, t) is None

```