def test__eis():
assert _eis(z).diff(z) == -_eis(z) + 1 / z
pytest.raises(ArgumentIndexError, lambda: _eis(x).fdiff(2))
assert _eis(1/z).series(z) == \
z + z**2 + 2*z**3 + 6*z**4 + 24*z**5 + O(z**6)
assert Ei(z).rewrite('tractable') == exp(z) * _eis(z)
assert li(z).rewrite('tractable') == z * _eis(log(z))
assert _eis(z).rewrite('intractable') == exp(-z) * Ei(z)
assert expand(li(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== li(z).diff(z)
assert expand(Ei(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== Ei(z).diff(z)
assert _eis(z).series(
z,
n=2) == EulerGamma + log(z) + z * (-log(z) - EulerGamma + 1) + z**2 * (
log(z) / 2 - Rational(3, 4) + EulerGamma / 2) + O(z**2)
l = Limit(Ei(y / x) / exp(y / x), x, 0)
assert l.doit() == l # cover _eis._eval_aseries
def test__eis():
assert _eis(z).diff(z) == -_eis(z) + 1/z
assert _eis(1/z).series(z) == \
z + z**2 + 2*z**3 + 6*z**4 + 24*z**5 + O(z**6)
assert Ei(z).rewrite('tractable') == exp(z)*_eis(z)
assert li(z).rewrite('tractable') == z*_eis(log(z))
assert _eis(z).rewrite('intractable') == exp(-z)*Ei(z)
assert expand(li(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== li(z).diff(z)
assert expand(Ei(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== Ei(z).diff(z)
assert _eis(z).series(z, n=2) == EulerGamma + log(z) + z*(-log(z) -
EulerGamma + 1) + z**2*(log(z)/2 - Rational(3, 4) + EulerGamma/2) + O(z**2)
def test__eis():
assert _eis(z).diff(z) == -_eis(z) + 1/z
pytest.raises(ArgumentIndexError, lambda: _eis(x).fdiff(2))
assert _eis(1/z).series(z) == \
z + z**2 + 2*z**3 + 6*z**4 + 24*z**5 + O(z**6)
assert Ei(z).rewrite('tractable') == exp(z)*_eis(z)
assert li(z).rewrite('tractable') == z*_eis(log(z))
assert _eis(z).rewrite('intractable') == exp(-z)*Ei(z)
assert expand(li(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== li(z).diff(z)
assert expand(Ei(z).rewrite('tractable').diff(z).rewrite('intractable')) \
== Ei(z).diff(z)
assert _eis(z).series(z, n=2) == EulerGamma + log(z) + z*(-log(z) -
EulerGamma + 1) + z**2*(log(z)/2 - Rational(3, 4) + EulerGamma/2) + O(z**2)
l = Limit(Ei(y/x)/exp(y/x), x, 0)
assert l.doit() == l # cover _eis._eval_aseries