# Argument selection and reproduction

Differentiation gives $\operatorname{Ci}^{\prime}(x)=\cos(x)/x$ CITE{NaturalArguments}; hence its positive extrema occur at $x=(2n-1)\pi/2$, $n\geq1$.

it holds the twenty extremal heights at $x=(2n-1)\pi/2$, $1\leq n\leq20$; the selection is not exhaustive over the real domain

References: https://dlmf.nist.gov/6.2

Install numberdb, python-flint and mpmath. Run `python generate.py` to verify the stored selection or `python checks.py T193 --live` for independent checks. The default never writes. `--fill` sends entries; `--remove-unselected` is a separate explicit choice. It does not approve or publish a table. Historical reference grids remain available in the website revision history.