* Bill Gosper <billgosper@gmail.com> [Aug 08. 2015 11:07]:
Both http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html (18) and https://en.wikipedia.org/wiki/Elliptic_integral#Differential_equation give K'[k] == E[k]/k/(1 - k^2) - K[k]/k .
This should be corrected (just did that) to d/dk K[k] == E[k]/k/(1 - k^2) - K[k]/k . (...if my relation (31.2-26a) on p.604 is correct). Apparently I lifted the 4 formulas shown from p.75 of Alfred Cardew Dixon: The elementary properties of the elliptic functions, with examples, Macmillan, (1894). http://www.archive.org/details/117736039 Best regards, jj
Both sources use the k (modulus) notation vs Mathematica's m (parameter) notation. But I can't find *any* interpretation that makes this work. I see no similar claim in DLMF nor Borwein*2. ?? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun