Spherical Bessel functions of the first kind are defined as,

from mpmath import mpf, sqrt, pi, besselj

def sph_jn(n, z):
    return besselj(n + mpf(1)/2, z)*sqrt(pi/(2*z))

For positive integer n, these functions have closed-form expressions in terms of trigonometric functions. For example, sph_jn(0, x) = sin(x)/x (see http://dlmf.nist.gov/10.49.E3).

For negative values of x, the mpmath implementation of these functions has the wrong sign. For example,

>>> sph_jn(0, -1)
mpc(real='-0.84147098480789639', imag='0.0')

The magnitude is correct, but the sign is not!

EDIT: The same problem plagues spherical Bessel functions of the second kind, defined analogously in terms of bessely.