def test_Li():
assert Li(2) == 0
assert Li(oo) is oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1 / log(z)
assert gruntz(1 / Li(z), z, oo) == 0
assert Li(z).rewrite(li) == li(z) - li(2)
assert Li(z).series(z) == \
log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + log(z) + log(log(z)) - li(2) + EulerGamma
raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1 / log(z)
assert gruntz(1 / Li(z), z, oo) == 0
assert Li(z).rewrite(li) == li(z) - li(2)
raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1/log(z)
assert gruntz(1/Li(z), z, oo) == 0
assert Li(z).rewrite(li) == li(z) - li(2)
def test_li():
z = Symbol("z")
zr = Symbol("z", real=True)
zp = Symbol("z", positive=True)
zn = Symbol("z", negative=True)
assert li(0) == 0
assert li(1) is -oo
assert li(oo) is oo
assert isinstance(li(z), li)
assert unchanged(li, -zp)
assert unchanged(li, zn)
assert diff(li(z), z) == 1 / log(z)
assert conjugate(li(z)) == li(conjugate(z))
assert conjugate(li(-zr)) == li(-zr)
assert unchanged(conjugate, li(-zp))
assert unchanged(conjugate, li(zn))
assert li(z).rewrite(Li) == Li(z) + li(2)
assert li(z).rewrite(Ei) == Ei(log(z))
assert li(z).rewrite(uppergamma) == (-log(1 / log(z)) / 2 - log(-log(z)) +
log(log(z)) / 2 - expint(1, -log(z)))
assert li(z).rewrite(Si) == (-log(I * log(z)) - log(1 / log(z)) / 2 +
log(log(z)) / 2 + Ci(I * log(z)) +
Shi(log(z)))
assert li(z).rewrite(Ci) == (-log(I * log(z)) - log(1 / log(z)) / 2 +
log(log(z)) / 2 + Ci(I * log(z)) +
Shi(log(z)))
assert li(z).rewrite(Shi) == (-log(1 / log(z)) / 2 + log(log(z)) / 2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(Chi) == (-log(1 / log(z)) / 2 + log(log(z)) / 2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(hyper) == (log(z) * hyper(
(1, 1),
(2, 2), log(z)) - log(1 / log(z)) / 2 + log(log(z)) / 2 + EulerGamma)
assert li(z).rewrite(meijerg) == (-log(1 / log(z)) / 2 - log(-log(z)) +
log(log(z)) / 2 - meijerg(
((), (1, )), ((0, 0), ()), -log(z)))
assert gruntz(1 / li(z), z, oo) == 0
assert li(z).series(z) == log(z)**5/600 + log(z)**4/96 + log(z)**3/18 + log(z)**2/4 + \
log(z) + log(log(z)) + EulerGamma
raises(ArgumentIndexError, lambda: li(z).fdiff(2))
def test_li():
z = Symbol("z")
zr = Symbol("z", real=True)
zp = Symbol("z", positive=True)
zn = Symbol("z", negative=True)
assert li(0) == 0
assert li(1) == -oo
assert li(oo) == oo
assert isinstance(li(z), li)
assert diff(li(z), z) == 1 / log(z)
assert conjugate(li(z)) == li(conjugate(z))
assert conjugate(li(-zr)) == li(-zr)
assert conjugate(li(-zp)) == conjugate(li(-zp))
assert conjugate(li(zn)) == conjugate(li(zn))
assert li(z).rewrite(Li) == Li(z) + li(2)
assert li(z).rewrite(Ei) == Ei(log(z))
assert li(z).rewrite(uppergamma) == (-log(1 / log(z)) / 2 - log(-log(z)) +
log(log(z)) / 2 - expint(1, -log(z)))
assert li(z).rewrite(Si) == (-log(I * log(z)) - log(1 / log(z)) / 2 +
log(log(z)) / 2 + Ci(I * log(z)) +
Shi(log(z)))
assert li(z).rewrite(Ci) == (-log(I * log(z)) - log(1 / log(z)) / 2 +
log(log(z)) / 2 + Ci(I * log(z)) +
Shi(log(z)))
assert li(z).rewrite(Shi) == (-log(1 / log(z)) / 2 + log(log(z)) / 2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(Chi) == (-log(1 / log(z)) / 2 + log(log(z)) / 2 +
Chi(log(z)) - Shi(log(z)))
assert li(z).rewrite(hyper) == (log(z) * hyper(
(1, 1),
(2, 2), log(z)) - log(1 / log(z)) / 2 + log(log(z)) / 2 + EulerGamma)
assert li(z).rewrite(meijerg) == (-log(1 / log(z)) / 2 - log(-log(z)) +
log(log(z)) / 2 - meijerg(
((), (1, )), ((0, 0), ()), -log(z)))
assert gruntz(1 / li(z), z, oo) == 0
