History of Values of the elliptic alpha function $\alpha(r)$

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when	who	what
2026-09-17 13:23	bmatschke	the link to T296 names it the way T296 now writes itself, K(m_r)	current reviewed
2026-09-17 13:08	bmatschke	entry comments cite Borwein and Borwein 1987, p. 172, the source MathWorld itself gives for these closed forms, and say which of them are derived: alpha(1) by Legendre's relation, alpha(4) and alpha(8) exactly from alpha(1) and alpha(2) by the order-two relation; the rest agree to 100 digits and are
2026-09-17 11:25	zeta3	shorten elliptic alpha definition after audit
2026-09-17 11:24	zeta3	restore definition and note the limit to 1/pi
2026-09-17 11:11	zeta3	shorten elliptic alpha definition
2026-09-17 11:09	zeta3 with codex-cli	elliptic alpha function values for r=1..100
2026-09-17 11:06	zeta3	proposed elliptic alpha function draft

What changed between 2026-09-17 13:08 and 2026-09-17 13:23

from line 80 (5 lines) @@ -80,5 +80,5 @@

   complete: 'no'   complete-note: it holds $\alpha(r)$ for every integer $1\leq r\leq100$, matching-    the range of HREF{T295}[the singular moduli $k_r$] and HREF{T296}[$K(k_r)$]; over+    the range of HREF{T295}[the singular moduli $k_r$] and HREF{T296}[$K(m_r)$]; over     this range the order $\mathbb Z[\sqrt{-r}]$ has class number at most $12$   rigour details: 'Each value is computed in Sage''s arb-backed `ComplexBallField`