def test_heurisch_hacking():
assert (heurisch(sqrt(1 + 7 * x**2), x,
hints=[]) == x * sqrt(1 + 7 * x**2) / 2 +
sqrt(7) * asinh(sqrt(7) * x) / 14)
assert (heurisch(sqrt(1 - 7 * x**2), x,
hints=[]) == x * sqrt(1 - 7 * x**2) / 2 +
sqrt(7) * asin(sqrt(7) * x) / 14)
assert heurisch(sqrt(y * x**2 - 1), x, hints=[]) is None
assert (heurisch(1 / sqrt(1 + 7 * x**2), x,
hints=[]) == sqrt(7) * asinh(sqrt(7) * x) / 7)
assert (heurisch(1 / sqrt(1 - 7 * x**2), x,
hints=[]) == sqrt(7) * asin(sqrt(7) * x) / 7)
assert heurisch(exp(-7 * x**2), x,
hints=[]) == sqrt(7 * pi) * erf(sqrt(7) * x) / 14
assert heurisch(exp(2 * x**2), x,
hints=[]) == sqrt(2) * sqrt(pi) * erfi(sqrt(2) * x) / 4
assert (heurisch(exp(2 * x**2 - 3 * x), x,
hints=[]) == sqrt(2) * sqrt(pi) *
erfi(sqrt(2) * x - 3 * sqrt(2) / 4) / (4 * E**Rational(9, 8)))
assert heurisch(1 / sqrt(9 - 4 * x**2), x, hints=[]) == asin(2 * x / 3) / 2
assert heurisch(1 / sqrt(9 + 4 * x**2), x,
hints=[]) == asinh(2 * x / 3) / 2
assert heurisch(li(x), x, hints=[]) == x * li(x) - Ei(2 * log(x))
assert heurisch(li(log(x)), x, hints=[]) is None
assert (heurisch(sqrt(1 + x), x,
hints=[x, sqrt(1 + x)]) == 2 * x * sqrt(x + 1) / 3 +
2 * sqrt(x + 1) / 3)
def test_ei():
pos = Symbol('p', positive=True)
neg = Symbol('n', negative=True)
assert Ei(0) == -oo
assert Ei(+oo) == oo
assert Ei(-oo) == 0
assert Ei(-pos) == Ei(polar_lift(-1)*pos) - I*pi
assert Ei(neg) == Ei(polar_lift(neg)) - I*pi
assert tn_branch(Ei)
assert mytd(Ei(x), exp(x)/x, x)
assert mytn(Ei(x), Ei(x).rewrite(uppergamma),
-uppergamma(0, x*polar_lift(-1)) - I*pi, x)
assert mytn(Ei(x), Ei(x).rewrite(expint),
-expint(1, x*polar_lift(-1)) - I*pi, x)
assert Ei(x).rewrite(expint).rewrite(Ei) == Ei(x)
assert Ei(x*exp_polar(2*I*pi)) == Ei(x) + 2*I*pi
assert Ei(x*exp_polar(-2*I*pi)) == Ei(x) - 2*I*pi
assert mytn(Ei(x), Ei(x).rewrite(Shi), Chi(x) + Shi(x), x)
assert mytn(Ei(x*polar_lift(I)), Ei(x*polar_lift(I)).rewrite(Si),
Ci(x) + I*Si(x) + I*pi/2, x)
assert Ei(log(x)).rewrite(li) == li(x)
assert Ei(2*log(x)).rewrite(li) == li(x**2)
assert Ei(x).series(x) == (EulerGamma + log(x) + x + x**2/4 +
x**3/18 + x**4/96 + x**5/600 + O(x**6))
assert Ei(1 + x).series(x) == (Ei(1) + E*x + E*x**3/6 - E*x**4/12 +
3*E*x**5/40 + O(x**6))
pytest.raises(ArgumentIndexError, lambda: Ei(x).fdiff(2))
def test_ei():
pos = Symbol('p', positive=True)
neg = Symbol('n', negative=True)
assert Ei(0) == -oo
assert Ei(+oo) == oo
assert Ei(-oo) == 0
assert Ei(-pos) == Ei(polar_lift(-1) * pos) - I * pi
assert Ei(neg) == Ei(polar_lift(neg)) - I * pi
assert tn_branch(Ei)
assert mytd(Ei(x), exp(x) / x, x)
assert mytn(Ei(x),
Ei(x).rewrite(uppergamma),
-uppergamma(0, x * polar_lift(-1)) - I * pi, x)
assert mytn(Ei(x),
Ei(x).rewrite(expint), -expint(1, x * polar_lift(-1)) - I * pi,
x)
assert Ei(x).rewrite(expint).rewrite(Ei) == Ei(x)
assert Ei(x * exp_polar(2 * I * pi)) == Ei(x) + 2 * I * pi
assert Ei(x * exp_polar(-2 * I * pi)) == Ei(x) - 2 * I * pi
assert mytn(Ei(x), Ei(x).rewrite(Shi), Chi(x) + Shi(x), x)
assert mytn(Ei(x * polar_lift(I)),
Ei(x * polar_lift(I)).rewrite(Si),
Ci(x) + I * Si(x) + I * pi / 2, x)
assert Ei(log(x)).rewrite(li) == li(x)
assert Ei(2 * log(x)).rewrite(li) == li(x**2)
assert Ei(x).series(x) == (EulerGamma + log(x) + x + x**2 / 4 + x**3 / 18 +
x**4 / 96 + x**5 / 600 + O(x**6))
assert Ei(1 + x).series(x) == (Ei(1) + E * x + E * x**3 / 6 -
E * x**4 / 12 + 3 * E * x**5 / 40 + O(x**6))
pytest.raises(ArgumentIndexError, lambda: Ei(x).fdiff(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
def test_ei():
pos = Symbol('p', positive=True)
neg = Symbol('n', negative=True)
assert Ei(-pos) == Ei(polar_lift(-1) * pos) - I * pi
assert Ei(neg) == Ei(polar_lift(neg)) - I * pi
assert tn_branch(Ei)
assert mytd(Ei(x), exp(x) / x, x)
assert mytn(Ei(x),
Ei(x).rewrite(uppergamma),
-uppergamma(0, x * polar_lift(-1)) - I * pi, x)
assert mytn(Ei(x),
Ei(x).rewrite(expint), -expint(1, x * polar_lift(-1)) - I * pi,
x)
assert Ei(x).rewrite(expint).rewrite(Ei) == Ei(x)
assert Ei(x * exp_polar(2 * I * pi)) == Ei(x) + 2 * I * pi
assert Ei(x * exp_polar(-2 * I * pi)) == Ei(x) - 2 * I * pi
assert mytn(Ei(x), Ei(x).rewrite(Shi), Chi(x) + Shi(x), x)
assert mytn(Ei(x * polar_lift(I)),
Ei(x * polar_lift(I)).rewrite(Si),
Ci(x) + I * Si(x) + I * pi / 2, x)
assert Ei(log(x)).rewrite(li) == li(x)
assert Ei(2 * log(x)).rewrite(li) == li(x**2)
assert Ei(x).series(x) == EulerGamma + log(x) + x + x**2/4 + \
x**3/18 + x**4/96 + x**5/600 + O(x**6)
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 Li(z).rewrite(li) == li(z) - li(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)
pytest.raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
assert Li(z).rewrite(li) == li(z) - li(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)
pytest.raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
assert Li(z).rewrite(li) == li(z) - li(2)
assert Li(4).evalf(30) == Float('1.92242131492155809316615998937961', dps=30)
def test_Li():
assert Li(2) == 0
assert Li(oo) == oo
assert isinstance(Li(z), Li)
assert diff(Li(z), z) == 1 / log(z)
pytest.raises(ArgumentIndexError, lambda: Li(z).fdiff(2))
assert Li(z).rewrite(li) == li(z) - li(2)
assert Li(4).evalf(30) == Float('1.92242131492155809316615998937961',
dps=30)
def test_specfun():
for f in [besselj, bessely, besseli, besselk]:
assert octave_code(f(n, x)) == f.__name__ + '(n, x)'
assert octave_code(hankel1(n, x)) == 'besselh(n, 1, x)'
assert octave_code(hankel2(n, x)) == 'besselh(n, 2, x)'
assert octave_code(airyai(x)) == 'airy(0, x)'
assert octave_code(airyaiprime(x)) == 'airy(1, x)'
assert octave_code(airybi(x)) == 'airy(2, x)'
assert octave_code(airybiprime(x)) == 'airy(3, x)'
assert octave_code(uppergamma(n, x)) == "gammainc(x, n, 'upper')"
assert octave_code(lowergamma(n, x)) == "gammainc(x, n, 'lower')"
assert octave_code(jn(
n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2'
assert octave_code(yn(
n, x)) == 'sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2'
assert octave_code(Chi(x)) == 'coshint(x)'
assert octave_code(Ci(x)) == 'cosint(x)'
assert octave_code(laguerre(n, x)) == 'laguerreL(n, x)'
assert octave_code(li(x)) == 'logint(x)'
assert octave_code(loggamma(x)) == 'gammaln(x)'
assert octave_code(polygamma(n, x)) == 'psi(n, x)'
assert octave_code(Shi(x)) == 'sinhint(x)'
assert octave_code(Si(x)) == 'sinint(x)'
assert octave_code(LambertW(x)) == 'lambertw(x)'
assert octave_code(LambertW(x, n)) == 'lambertw(n, x)'
assert octave_code(zeta(x)) == 'zeta(x)'
assert octave_code(zeta(
x, y)) == '% Not supported in Octave:\n% zeta\nzeta(x, y)'
def test_limit():
assert gruntz(x, x) == oo
assert gruntz(-x, x) == -oo
assert gruntz(-x, x) == -oo
assert gruntz((-x)**2, x) == oo
assert gruntz(-x**2, x) == -oo
assert gruntz((1/x)*log(1/x), x) == 0 # Gruntz: p15, 2.11
assert gruntz(1/x, x) == 0
assert gruntz(exp(x), x) == oo
assert gruntz(-exp(x), x) == -oo
assert gruntz(exp(x)/x, x) == oo
assert gruntz(1/x - exp(-x), x) == 0
assert gruntz(x + 1/x, x) == oo
assert gruntz((1/x)**(1/x), x) == 1 # Gruntz: p15, 2.11
assert gruntz((exp(1/x) - 1)*x, x) == 1
assert gruntz(1 + 1/x, x) == 1
assert gruntz(-exp(1/x), x) == -1
assert gruntz(x + exp(-x), x) == oo
assert gruntz(x + exp(-x**2), x) == oo
assert gruntz(x + exp(-exp(x)), x) == oo
assert gruntz(13 + 1/x - exp(-x), x) == 13
a = Symbol('a')
assert gruntz(x - log(1 + exp(x)), x) == 0
assert gruntz(x - log(a + exp(x)), x) == 0
assert gruntz(exp(x)/(1 + exp(x)), x) == 1
assert gruntz(exp(x)/(a + exp(x)), x) == 1
assert gruntz((3**x + 5**x)**(1/x), x) == 5 # issue sympy/sympy#3463
assert gruntz(Ei(x + exp(-x))*exp(-x)*x, x) == 1
assert gruntz(1/li(x), x) == 0
assert gruntz(1/Li(x), x) == 0
# issue diofant/diofant#56
assert gruntz((log(E + 1/x) - 1)**(1 - sqrt(E + 1/x)), x) == oo
# issue sympy/sympy#9471
assert gruntz((((27**(log(x, 3))))/x**3), x) == 1
assert gruntz((((27**(log(x, 3) + 1)))/x**3), x) == 27
# issue sympy/sympy#9449
y = Symbol('y')
assert gruntz(x*(abs(1/x + y) - abs(y - 1/x))/2, x) == sign(y)
# issue sympy/sympy#8481
assert gruntz(m**x * exp(-m) / factorial(x), x) == 0
# issue sympy/sympy#4187
assert gruntz(exp(1/x)*log(1/x) - Ei(1/x), x) == -EulerGamma
assert gruntz(exp(x)*log(x) - Ei(x), x) == oo
# issue sympy/sympy#10382
assert gruntz(fibonacci(x + 1)/fibonacci(x), x) == GoldenRatio
assert gruntz(zeta(x), x) == 1
assert gruntz(zeta(m)*zeta(x), x) == zeta(m)
def test_limit():
assert gruntz(x, x) == oo
assert gruntz(-x, x) == -oo
assert gruntz(-x, x) == -oo
assert gruntz((-x)**2, x) == oo
assert gruntz(-x**2, x) == -oo
assert gruntz((1 / x) * log(1 / x), x) == 0 # Gruntz: p15, 2.11
assert gruntz(1 / x, x) == 0
assert gruntz(exp(x), x) == oo
assert gruntz(-exp(x), x) == -oo
assert gruntz(exp(x) / x, x) == oo
assert gruntz(1 / x - exp(-x), x) == 0
assert gruntz(x + 1 / x, x) == oo
assert gruntz((1 / x)**(1 / x), x) == 1 # Gruntz: p15, 2.11
assert gruntz((exp(1 / x) - 1) * x, x) == 1
assert gruntz(1 + 1 / x, x) == 1
assert gruntz(-exp(1 / x), x) == -1
assert gruntz(x + exp(-x), x) == oo
assert gruntz(x + exp(-x**2), x) == oo
assert gruntz(x + exp(-exp(x)), x) == oo
assert gruntz(13 + 1 / x - exp(-x), x) == 13
a = Symbol('a')
assert gruntz(x - log(1 + exp(x)), x) == 0
assert gruntz(x - log(a + exp(x)), x) == 0
assert gruntz(exp(x) / (1 + exp(x)), x) == 1
assert gruntz(exp(x) / (a + exp(x)), x) == 1
assert gruntz((3**x + 5**x)**(1 / x), x) == 5 # issue sympy/sympy#3463
assert gruntz(Ei(x + exp(-x)) * exp(-x) * x, x) == 1
assert gruntz(1 / li(x), x) == 0
assert gruntz(1 / Li(x), x) == 0
# issue diofant/diofant#56
assert gruntz((log(E + 1 / x) - 1)**(1 - sqrt(E + 1 / x)), x) == oo
# issue sympy/sympy#9471
assert gruntz((((27**(log(x, 3)))) / x**3), x) == 1
assert gruntz((((27**(log(x, 3) + 1))) / x**3), x) == 27
# issue sympy/sympy#9449
y = Symbol('y')
assert gruntz(x * (abs(1 / x + y) - abs(y - 1 / x)) / 2, x) == sign(y)
# issue sympy/sympy#8481
assert gruntz(m**x * exp(-m) / factorial(x), x) == 0
# issue sympy/sympy#4187
assert gruntz(exp(1 / x) * log(1 / x) - Ei(1 / x), x) == -EulerGamma
assert gruntz(exp(x) * log(x) - Ei(x), x) == oo
# issue sympy/sympy#10382
assert gruntz(fibonacci(x + 1) / fibonacci(x), x) == GoldenRatio
assert gruntz(zeta(x), x) == 1
assert gruntz(zeta(m) * zeta(x), x) == zeta(m)
def test_heurisch_hacking():
assert (heurisch(sqrt(1 + 7*x**2), x, hints=[]) ==
x*sqrt(1 + 7*x**2)/2 + sqrt(7)*asinh(sqrt(7)*x)/14)
assert (heurisch(sqrt(1 - 7*x**2), x, hints=[]) ==
x*sqrt(1 - 7*x**2)/2 + sqrt(7)*asin(sqrt(7)*x)/14)
assert (heurisch(1/sqrt(1 + 7*x**2), x, hints=[]) ==
sqrt(7)*asinh(sqrt(7)*x)/7)
assert (heurisch(1/sqrt(1 - 7*x**2), x, hints=[]) ==
sqrt(7)*asin(sqrt(7)*x)/7)
assert (heurisch(exp(-7*x**2), x, hints=[]) == sqrt(7*pi)*erf(sqrt(7)*x)/14)
assert heurisch(1/sqrt(9 - 4*x**2), x, hints=[]) == asin(2*x/3)/2
assert heurisch(1/sqrt(9 + 4*x**2), x, hints=[]) == asinh(2*x/3)/2
assert heurisch(li(x), x, hints=[]) == x*li(x) - Ei(2*log(x))
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_heurisch_hacking():
assert (heurisch(sqrt(1 + 7 * x**2), x,
hints=[]) == x * sqrt(1 + 7 * x**2) / 2 +
sqrt(7) * asinh(sqrt(7) * x) / 14)
assert (heurisch(sqrt(1 - 7 * x**2), x,
hints=[]) == x * sqrt(1 - 7 * x**2) / 2 +
sqrt(7) * asin(sqrt(7) * x) / 14)
assert (heurisch(1 / sqrt(1 + 7 * x**2), x,
hints=[]) == sqrt(7) * asinh(sqrt(7) * x) / 7)
assert (heurisch(1 / sqrt(1 - 7 * x**2), x,
hints=[]) == sqrt(7) * asin(sqrt(7) * x) / 7)
assert (heurisch(exp(-7 * x**2), x,
hints=[]) == sqrt(7 * pi) * erf(sqrt(7) * x) / 14)
assert heurisch(1 / sqrt(9 - 4 * x**2), x, hints=[]) == asin(2 * x / 3) / 2
assert heurisch(1 / sqrt(9 + 4 * x**2), x,
hints=[]) == asinh(2 * x / 3) / 2
assert heurisch(li(x), x, hints=[]) == x * li(x) - Ei(2 * log(x))
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_li():
z = Symbol('z')
zr = Symbol('z', extended_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)
pytest.raises(ArgumentIndexError, lambda: li(z).fdiff(2))
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)))
def test_li():
z = Symbol("z")
zr = Symbol("z", extended_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)
pytest.raises(ArgumentIndexError, lambda: li(z).fdiff(2))
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)))
