History of Values of the Clausen functions $\mathrm{Cl}_s$ at rational multiples of $\pi$

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2026-09-09 12:20 zeta3 kept Clausen rigour note about verification current reviewed
2026-09-09 12:15 zeta3 kept Clausen definition within the audit limit
2026-09-09 12:12 zeta3 clarified Clausen symmetry and special values
2026-09-09 11:45 zeta3 restored Clausen entries to record form
2026-09-09 11:42 zeta3 shortened the Clausen definition after audit
2026-09-09 11:36 zeta3 with code Clausen values at rational multiples of pi
2026-09-09 11:36 zeta3 checking that this table can be written to
2026-09-09 11:33 zeta3 proposed Clausen values at rational multiples of pi

What changed between 2026-09-09 12:15 and 2026-09-09 12:20

from line 131 (9 lines, 2 fewer than before) @@ -131,11 +131,9 @@
   rigour details: Each value was computed as a Sage complex ball with arb at `numberdb.bits(digits,     losing=96)` bits by evaluating $\mathrm{Li}_s(e^{i\pi t})$ and taking the real-    or imaginary part specified in the definition. Before the draft was created, all-    538 entries agreed as written with the Hurwitz-zeta decomposition CITE{formula-hurwitz};-    the special values in CITE{formula-special-values} agreed with independent zeta-    and Hurwitz-zeta computations, and the decimal prefixes for Catalan's constant,-    Gieseking's constant and $\mathrm{Cl}_2(2\pi/3)$ agreed with CITE{OEISCatalan},-    CITE{OEISGieseking} and CITE{OEISClausenTwoThirds}. The dry run measured 538 entries,-    a longest written entry of 105 characters, and a 76.4 KB entries block.+    or imaginary part specified in the definition. The 538 entries were checked against+    the Hurwitz-zeta decomposition CITE{formula-hurwitz}; the special values in CITE{formula-special-values}+    were checked against independent zeta, Hurwitz-zeta and Dirichlet $L$-value computations,+    and the decimal prefixes for Catalan's constant, Gieseking's constant and $\mathrm{Cl}_2(2\pi/3)$+    agreed with CITE{OEISCatalan}, CITE{OEISGieseking} and CITE{OEISClausenTwoThirds}.   complete: 'no'   complete-note: it holds every entry with $s\in\{2,3,4\}$ and $t=a/b$ in lowest terms 

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