def test_trigamma_expand_func():
assert (
trigamma(2 * x).expand(func=True)
== polygamma(1, x) / 4 + polygamma(1, Rational(1, 2) + x) / 4
)
assert trigamma(1 + x).expand(func=True) == polygamma(1, x) - 1 / x ** 2
assert (
trigamma(2 + x).expand(func=True, multinomial=False)
== polygamma(1, x) - 1 / x ** 2 - 1 / (1 + x) ** 2
)
assert (
trigamma(3 + x).expand(func=True, multinomial=False)
== polygamma(1, x) - 1 / x ** 2 - 1 / (1 + x) ** 2 - 1 / (2 + x) ** 2
)
assert (
trigamma(4 + x).expand(func=True, multinomial=False)
== polygamma(1, x)
- 1 / x ** 2
- 1 / (1 + x) ** 2
- 1 / (2 + x) ** 2
- 1 / (3 + x) ** 2
)
assert trigamma(x + y).expand(func=True) == polygamma(1, x + y)
assert (
trigamma(3 + 4 * x + y).expand(func=True, multinomial=False)
== polygamma(1, y + 4 * x)
- 1 / (y + 4 * x) ** 2
- 1 / (1 + y + 4 * x) ** 2
- 1 / (2 + y + 4 * x) ** 2
)
def test_trigamma():
assert trigamma(nan) == nan
assert trigamma(oo) == 0
assert trigamma(1) == pi**2 / 6
assert trigamma(2) == pi**2 / 6 - 1
assert trigamma(3) == pi**2 / 6 - Rational(5, 4)
assert trigamma(x, evaluate=False).rewrite(zeta) == zeta(2, x)
assert trigamma(x, evaluate=False).rewrite(harmonic) == \
trigamma(x).rewrite(polygamma).rewrite(harmonic)
assert trigamma(x, evaluate=False).fdiff() == polygamma(2, x)
assert trigamma(x, evaluate=False).is_real is None
assert trigamma(x, evaluate=False).is_positive is None
assert trigamma(x, evaluate=False).is_negative is None
assert trigamma(x, evaluate=False).rewrite(polygamma) == polygamma(1, x)
