def jv(v, x):
"""Bessel function J_v(x)."""
if isint(v):
if isinstance(x, mpf):
return make_mpf(libhyper.mpf_besseljn(int(v), x._mpf_, mp.prec))
if isinstance(x, mpc):
return make_mpc(libhyper.mpc_besseljn(int(v), x._mpc_, mp.prec))
hx = x/2
return hx**v * hyp0f1(v+1, -hx**2) / factorial(v)
def jv(v, x):
"""Bessel function J_v(x)."""
if isint(v):
if isinstance(x, mpf):
return make_mpf(libhyper.mpf_besseljn(int(v), x._mpf_, mp.prec))
if isinstance(x, mpc):
return make_mpc(libhyper.mpc_besseljn(int(v), x._mpc_, mp.prec))
hx = x / 2
return hx**v * hyp0f1(v + 1, -hx**2) / factorial(v)
def legendre(n, x):
"""Legendre polynomial P_n(x)."""
if isint(n):
n = int(n)
if x == -1:
# TODO: hyp2f1 should handle this
if x == int(x):
return (-1)**(n + (n>=0)) * mpf(-1)
return inf
return hyp2f1(-n,n+1,1,(1-x)/2)
def legendre(n, x):
"""Legendre polynomial P_n(x)."""
if isint(n):
n = int(n)
if x == -1:
# TODO: hyp2f1 should handle this
if x == int(x):
return (-1)**(n + (n >= 0)) * mpf(-1)
return inf
return hyp2f1(-n, n + 1, 1, (1 - x) / 2)
