Version Information:
Julia 1.11.4
SpecialFunctions v2.5.0
zeta(s, z) gives incorrect values in the region $\Re (z) \geq 7 + \Re (s - 1) + |\Im (s) |$. For example:
julia> zeta(-13+7im, 0.5) # should be ~350.218774132674 + 259.188383123717im
-3371.4397140865763 + 2764.0891272966132im
The function jumps sharply at the boundary of the affected region and no longer behaves as expected. You can see the effects in these plots (using z=0.5):
If my understanding is correct, the Euler-Maclaurin expansion used should be well-defined for $\Re(s) \gt -17$ or so. However, I think the initial sum is prematurely truncated to zero terms when the cutoff is checked.
Version Information:
Julia 1.11.4
SpecialFunctions v2.5.0
zeta(s, z)gives incorrect values in the regionThe function jumps sharply at the boundary of the affected region and no longer behaves as expected. You can see the effects in these plots (using z=0.5):
If my understanding is correct, the Euler-Maclaurin expansion used should be well-defined for$\Re(s) \gt -17$ or so. However, I think the initial sum is prematurely truncated to zero terms when the cutoff is checked.