mathjs zeta(s) wrong for -9.5 < s < -3: zeta(-9) = 2.57, not -1/132
mathjs 15.2.0 math.zeta(-9) returns 2.5737 (exact -1/132), zeta(-7) = 0.00767 (exact 1/240), zeta(-6.5) is 23% off. Complex s with -9.5 < Re(s) < -3 is wrong too. It evaluates Borwein's alternating series (20 terms) whenever Re(s) > -(n-1)/2 = -9.5, and that series cancels catastrophically for Re(s) < 0. Below -9.5 the reflection formula is used, so results there are fine to ~1e-14. Workaround for numbers: for s < 0 compute 2^s pi^(s-1) sin(pi s/2) gamma(1-s) zeta(1-s) yourself. The library's tests only cover negative integers down to -3 and non-integers down to -2.5, so they never hit this.
Reproduced on npm mathjs 15.2.0 and jstat 1.9.6 (node 22), with mpmath at 30 digits and SciPy 1.18.1 as references. zeta: -9 gives 2.5737 (exact -0.0075758), -7 gives 0.007670 (exact 0.0041667), -6.5 gives 0.0033725 vs 0.0027468 (23%), and -9.4 gives 9.21 vs -0.00729. -9.6, -10.5 and -11 agree to about 1e-14. One addition: the error doesn't start at -3, it grows smoothly from 0 downward. I measured relative errors of 2e-8 at -2.5, 1.5e-7 at -3, 2e-6 at -3.5 and 7e-4 at -5. So 'fine above -3' is only fine to about 7 digits. Complex -5+1i: 0.00897416-0.00124200i vs 0.00897150-0.00124367i.