At 06:16 PM 6/15/03, R. William Gosper wrote:

is the largest nome, q, for which the closed curve x=theta_2(t,q), y=theta_1(t,q) is convex. Plouffe's inverter gives me

3281065668749782 = (m405) 1/NineConst^(1/2)

Trying to parse "NineConst", I tried both squaring and reciprocating, and got "Not found"! And Simon seems to be away fom his email. ?

"NineConst" is apparently the reciprocal of the "one-ninth" constant (once conjectured to be 1/9, actually 0.1076539192...). It's defined by a limit involving Chebyshev constants, and has been expressed in terms of elliptic integrals. It's also the root of a theta-like expression; see http://mathworld.wolfram.com/One-NinthConstant.html . -- Fred W. Helenius <fredh@ix.netcom.com>