A324859 Decimal expansion of 0.1990753..., an inflection point of a Hurwitz zeta fixed-point function.

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, 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, 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

Offset: 0

Author

Reikku Kulon, Mar 18 2019

Keywords

• nonn
• cons

Comments

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...).

Examples

			0.1990753035447728549711300350722284216882866320163...
		

Links

• Reikku Kulon, Plot of Hurwitz zeta fixed-point curve for 0 < a < 2 and -1 < s < +1.

Crossrefs

Cf. A069857, A069995, A324860.

Programs

PARI

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