back to table · edit · history · where entries came from · files · download
1605 bytes, as of the version from 2026-10-26 15:42 (current). Recorded here, not run.
# Argument selection for T246
The integer orders are the logarithmic forms of the integer zeta special values and derivatives CITE{SelectionIntegerZeta}; the nonpositive even zeros are excluded. At the functional-equation centre, $\zeta'(1/2)/\zeta(1/2)=(\log\pi-\psi(1/4))/2$ CITE{SelectionZetaSymmetry}. The integer interval is a finite reference prefix; denominator bounds alone do not select additional orders.
Coverage: it holds the integer arguments $-20\leq s\leq20$ where the quotient is finite, and $s=1/2$; these are the integer special-value references and the functional-equation centre, not a continuous rational grid.
## Primary mathematical evidence
- DLMF 25.6: Integer Arguments and Derivatives: https://dlmf.nist.gov/25.6
- DLMF 25.4: Reflection Formulas: https://dlmf.nist.gov/25.4
The mathematical deductions in the selection paragraph are distinguished from a source publishing this exact finite list. The range cutoff is a reference limit, not a theorem that every included dimension or order has a separate documented application.
## Reproduction and history
Run `python generate.py` to verify and `python checks.py T246 --live` for independent checks. Neither writes. The source uses exact rational arithmetic and certified Arb balls, with mpmath as a separate agreement check. Retained numeric strings and annotations are copied from, and verified against, the website export; the generator is not claimed to have authored those annotations. Removed sample identities and old attached sources remain in website revision history. No identity is reused for another argument.