History of Complete elliptic integral of the first kind $K(m_r)$ at the singular values

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when	who	what
2026-09-17 13:23	bmatschke	the Polya relation wrote K(k_6) where this table writes K(m_6)	current reviewed
2026-09-17 13:23	bmatschke	one notation for K: the parameter m_r = k_r^2 throughout -- title, column header, entry comments, notes -- matching the corpus's table of K(m), the alpha-function table, and this table's own equals link to K(m) at m = 1/2. The classical modulus notation K(k_r) is kept in one place, the convention co
2026-09-17 10:00	zeta3	shorten definition after audit warning
2026-09-17 10:00	zeta3	repair notation, range note, and broken singular-value comment
2026-09-17 09:45	zeta3	shorten T296 definition
2026-09-17 09:43	zeta3 with codex-cli	complete elliptic integrals at singular values for r=1..100
2026-09-17 09:39	zeta3	claim K(k_r) singular-value draft

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

from line 56 (5 lines) @@ -56,5 +56,5 @@

 - table: HREF{Polya's_random_walk_constants}[Pólya's random walk constants]   relation: the return probability is $p(3)=1-1/u(3)$, where Watson's integral is-    $u(3)=\frac{12}{\pi^2}(18+12\sqrt2-10\sqrt3-7\sqrt6)K(k_6)^2$+    $u(3)=\frac{12}{\pi^2}(18+12\sqrt2-10\sqrt3-7\sqrt6)K(m_6)^2$ Links:   DLMFEllipticIntegrals: