def test_meijer(): raises(TypeError, lambda: meijerg(1, z)) raises(TypeError, lambda: meijerg(((1,), (2,)), (3,), (4,), z)) assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z) g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z) assert g.an == Tuple(1, 2) assert g.ap == Tuple(1, 2, 3, 4, 5) assert g.aother == Tuple(3, 4, 5) assert g.bm == Tuple(6, 7, 8, 9) assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14) assert g.bother == Tuple(10, 11, 12, 13, 14) assert g.argument == z assert g.nu == 75 assert g.delta == -1 assert g.is_commutative is True assert meijerg([1, 2], [3], [4], [5], z).delta == S(1) / 2 # just a few checks to make sure that all arguments go where they should assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z) assert tn(sqrt(pi) * meijerg(Tuple(), Tuple(), Tuple(0), Tuple(S(1) / 2), z ** 2 / 4), cos(z), z) assert tn(meijerg(Tuple(1, 1), Tuple(), Tuple(1), Tuple(0), z), log(1 + z), z) # differentiation g = meijerg((randcplx(),), (randcplx() + 2 * I,), Tuple(), (randcplx(), randcplx()), z) assert td(g, z) g = meijerg(Tuple(), (randcplx(),), Tuple(), (randcplx(), randcplx()), z) assert td(g, z) g = meijerg(Tuple(), Tuple(), Tuple(randcplx()), Tuple(randcplx(), randcplx()), z) assert td(g, z) a1, a2, b1, b2, c1, c2, d1, d2 = symbols("a1:3, b1:3, c1:3, d1:3") assert ( meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == ( meijerg((a1 - 1, a2), (b1, b2), (c1, c2), (d1, d2), z) + (a1 - 1) * meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z) ) / z ) assert meijerg([z, z], [], [], [], z).diff(z) == Derivative(meijerg([z, z], [], [], [], z), z) # meijerg is unbranched wrt parameters from sympy import polar_lift as pl assert meijerg([pl(a1)], [pl(a2)], [pl(b1)], [pl(b2)], pl(z)) == meijerg([a1], [a2], [b1], [b2], pl(z)) # integrand from sympy.abc import a, b, c, d, s assert meijerg([a], [b], [c], [d], z).integrand(s) == z ** s * gamma(c - s) * gamma(-a + s + 1) / ( gamma(b - s) * gamma(-d + s + 1) )
def test_meijer(): raises(TypeError, lambda: meijerg(1, z)) raises(TypeError, lambda: meijerg(((1, ), (2, )), (3, ), (4, ), z)) assert meijerg(((1, 2), (3,)), ((4,), (5,)), z) == \ meijerg(Tuple(1, 2), Tuple(3), Tuple(4), Tuple(5), z) g = meijerg((1, 2), (3, 4, 5), (6, 7, 8, 9), (10, 11, 12, 13, 14), z) assert g.an == Tuple(1, 2) assert g.ap == Tuple(1, 2, 3, 4, 5) assert g.aother == Tuple(3, 4, 5) assert g.bm == Tuple(6, 7, 8, 9) assert g.bq == Tuple(6, 7, 8, 9, 10, 11, 12, 13, 14) assert g.bother == Tuple(10, 11, 12, 13, 14) assert g.argument == z assert g.nu == 75 assert g.delta == -1 assert g.is_commutative is True assert meijerg([1, 2], [3], [4], [5], z).delta == S(1) / 2 # just a few checks to make sure that all arguments go where they should assert tn(meijerg(Tuple(), Tuple(), Tuple(0), Tuple(), -z), exp(z), z) assert tn( sqrt(pi) * meijerg(Tuple(), Tuple(), Tuple(0), Tuple(S(1) / 2), z**2 / 4), cos(z), z) assert tn(meijerg(Tuple(1, 1), Tuple(), Tuple(1), Tuple(0), z), log(1 + z), z) # differentiation g = meijerg((randcplx(), ), (randcplx() + 2 * I, ), Tuple(), (randcplx(), randcplx()), z) assert td(g, z) g = meijerg(Tuple(), (randcplx(), ), Tuple(), (randcplx(), randcplx()), z) assert td(g, z) g = meijerg(Tuple(), Tuple(), Tuple(randcplx()), Tuple(randcplx(), randcplx()), z) assert td(g, z) a1, a2, b1, b2, c1, c2, d1, d2 = symbols('a1:3, b1:3, c1:3, d1:3') assert meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z).diff(z) == \ (meijerg((a1 - 1, a2), (b1, b2), (c1, c2), (d1, d2), z) + (a1 - 1)*meijerg((a1, a2), (b1, b2), (c1, c2), (d1, d2), z))/z assert meijerg([z, z], [], [], [], z).diff(z) == \ Derivative(meijerg([z, z], [], [], [], z), z) # meijerg is unbranched wrt parameters from sympy import polar_lift as pl assert meijerg([pl(a1)], [pl(a2)], [pl(b1)], [pl(b2)], pl(z)) == \ meijerg([a1], [a2], [b1], [b2], pl(z)) # integrand from sympy.abc import a, b, c, d, s assert meijerg([a], [b], [c], [d], z).integrand(s) == \ z**s*gamma(c - s)*gamma(-a + s + 1)/(gamma(b - s)*gamma(-d + s + 1))