A324859 - OEIS

%I #20 Mar 24 2019 06:08:04

%S 1,9,9,0,7,5,3,0,3,5,4,4,7,7,2,8,5,4,9,7,1,1,3,0,0,3,5,0,7,2,2,2,8,4,

%T 2,1,6,8,8,2,8,6,6,3,2,0,1,6,3,1,5,1,0,7,6,1,0,1,4,8,1,0,1,7,7,9,7,0,

%U 6,9,3,8,2,0,3,4,0,7,2,1,0,3,6,6,9,8,1,6,4,0,4,4,7,4,9,2,4,1,9,7

%N Decimal expansion of 0.1990753..., an inflection point of a Hurwitz zeta fixed-point function.

%C For real values of the parameter "a" between 0 and 1, a real fixed point "s" of the iterated Hurwitz zeta function [s = zetahurwitz(s, a)] lies on a curve that passes through A069857 (-0.295905...) and has a maximum tending toward 1.  This curve has inflection points for a = 0.1990753... or 0.91964... .  The fixed point "s" on this curve for the iteration "s = zetahurwitz(s, A324859)" is A324860 (0.5250984...).

%H Reikku Kulon, <a href="/A324859/a324859.png">Plot of Hurwitz zeta fixed-point curve</a> for 0 < a < 2 and -1 < s < +1.

%e 0.1990753035447728549711300350722284216882866320163...

%o (PARI) solve(t = 1/16, 1/2, derivnum(x = t, solve(v = -1, 1 - x, v - zetahurwitz(v, x)), 2); )

%Y Cf. A069857, A069995, A324860.

%K nonn,cons

%O 0,2

%A _Reikku Kulon_, Mar 18 2019