def test_polygamma():
x = Symbol("x")
y = Symbol("y")
e1 = sympy.polygamma(sympy.Symbol("x"), sympy.Symbol("y"))
e2 = polygamma(x, y)
assert sympify(e1) == e2
assert e2._sympy_() == e1
def test_S():
assert S(0) == Integer(0)
assert S(1) == Integer(1)
assert S(-1) == Integer(-1)
assert S(1) / 2 == Rational(1, 2)
assert S.One is S(1)
assert S.Zero is S(0)
assert S.NegativeOne is S(-1)
assert S.Half is S(1) / 2
assert S.Pi is pi
assert S.NaN is S(0) / 0
assert S.Infinity is -oo * -10
assert S.NegativeInfinity is oo * (-3)
assert S.ComplexInfinity is zoo
assert S.Exp1 is (E + 1 - 1)
assert S.ImaginaryUnit is sqrt(-1)
assert S.GoldenRatio * 2 / 2 is GoldenRatio
assert S.Catalan * 1 is Catalan
assert S.EulerGamma is polygamma(0, 1) * -1
assert S.true is Eq(2, 2)
assert S.false is Eq(2, 3)
assert S(1) / 0 is zoo
assert S.Pi * 1 is pi
assert type(S.One) == One
def test_trigamma():
x = Symbol("x")
assert trigamma(-2) == zoo
assert trigamma(x) == polygamma(1, x)
def test_digamma():
x = Symbol("x")
assert digamma(x) == polygamma(0, x)
assert digamma(0) == zoo
assert digamma(1) == -EulerGamma
def test_polygamma():
assert polygamma(0, -9) == zoo
assert polygamma(0, -9) == zoo
assert polygamma(0, -1) == zoo
assert polygamma(0, 0) == zoo
assert polygamma(0, 1) == -EulerGamma
assert polygamma(0, 7) == Rational(49, 20) - EulerGamma
assert polygamma(1, 1) == pi**2 / 6
assert polygamma(1, 2) == pi**2 / 6 - 1
assert polygamma(1, 3) == pi**2 / 6 - Rational(5, 4)
assert polygamma(3, 1) == pi**4 / 15
assert polygamma(3, 5) == 6 * (Rational(-22369, 20736) + pi**4 / 90)
assert polygamma(5, 1) == 8 * pi**6 / 63