def test_jacobi(self):
assert_mpmath_equal(sc.eval_jacobi,
_exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
[Arg(), Arg(), Arg(), Arg()])
assert_mpmath_equal(lambda n, b, c, x: sc.eval_jacobi(int(n), b, c, x),
_exception_to_nan(lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
[IntArg(), Arg(), Arg(), Arg()])
def test_jacobi(self):
assert_mpmath_equal(
sc.eval_jacobi,
_exception_to_nan(
lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
[Arg(), Arg(), Arg(), Arg()])
assert_mpmath_equal(
lambda n, b, c, x: sc.eval_jacobi(int(n), b, c, x),
_exception_to_nan(
lambda a, b, c, x: mpmath.jacobi(a, b, c, x, **HYPERKW)),
[IntArg(), Arg(), Arg(), Arg()])
def swaL(spin:int,m_ang:int,l_ang:int,x:float)->mp.mpf:
al= mp.mpf(abs(m_ang-spin))
be= mp.mpf(abs(m_ang+spin))
assert((al+be)%2==0)
n= mp.mpf(l_ang - (al+be)/2)
if n<0:
return mp.mpf(0)
norm= mp.sqrt(
(2*n+al+be+1)*mp.power(2,-al-be-1)
* mp.fdiv(mp.fac(n+al+be),mp.fac(n+al))
* mp.fdiv(mp.fac(n) ,mp.fac(n+be))
)
norm*= mp.power(-1,max(m_ang,-spin))
return norm*mp.power(1-x,al/2.)*mp.power(1+x,be/2.)*mp.jacobi(n,al,be,x)
