Fix premature truncation of the recurrence sum in zeta(s,z). #489
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Skipping the recurrence sum or truncating early causes the function to break inside a region determined by shape of the cutoff.
Codecov ReportAll modified and coverable lines are covered by tests ✅
Additional details and impacted files@@ Coverage Diff @@
## master #489 +/- ##
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- Coverage 94.11% 94.10% -0.01%
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Files 14 14
Lines 2905 2902 -3
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- Hits 2734 2731 -3
Misses 171 171
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As descriped in issue #488, skipping the recurrence sum or truncating early causes the function to break inside a region determined by shape of the cutoff. This rewrite also fixes another bug I encountered: sometimes the zero denominator term wasn't actually skipped, which caused sporadic failures.
This plot shows an example of how the error is improved relative to$(2^s-1)\zeta(s)$ in the affected area:
The accuracy still isn't perfect but the major breakage is fixed. Hopefully it can be improved in the future.