def test_catalan():
assert catalan(1) == 1
assert catalan(2) == 2
assert catalan(3) == 5
assert catalan(4) == 14
# assert catalan(x) == catalan(x)
assert catalan(2*x).rewrite(binomial) == binomial(4*x, 2*x)/(2*x + 1)
assert catalan(Rational(1,2)).rewrite(gamma) == 8/(3*pi)
assert catalan(3*x).rewrite(gamma) == 4**(3*x)*gamma(3*x + Rational(1,2))/(sqrt(pi)*gamma(3*x + 2))
assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2,), 1)
assert diff(catalan(x),x) == (polygamma(0, x + Rational(1,2)) - polygamma(0, x + 2) + 2*log(2))*catalan(x)
c = catalan(0.5).evalf()
assert str(c) == '0.848826363156775'
def test_latex_numbers():
assert latex(catalan(n)) == r"C_{n}"
def test_latex_numbers():
assert latex(catalan(n)) == r"C_{n}"
def test_catalan():
assert catalan(1) == 1
assert catalan(2) == 2
assert catalan(3) == 5
assert catalan(4) == 14
assert catalan(x) == catalan(x)
assert catalan(2 *
x).rewrite(binomial) == binomial(4 * x, 2 * x) / (2 * x + 1)
assert catalan(Rational(1, 2)).rewrite(gamma) == 8 / (3 * pi)
assert catalan(3 * x).rewrite(gamma) == 4**(
3 * x) * gamma(3 * x + Rational(1, 2)) / (sqrt(pi) * gamma(3 * x + 2))
assert catalan(x).rewrite(hyper) == hyper((-x + 1, -x), (2, ), 1)
assert diff(catalan(x), x) == (polygamma(0, x + Rational(1, 2)) -
polygamma(0, x + 2) + log(4)) * catalan(x)
c = catalan(0.5).evalf()
assert str(c) == '0.848826363156775'