A324860 Decimal expansion of 0.5250984..., a real fixed point of the iteration s = zetahurwitz(s, A324859).

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

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... (A324859) or 0.91964... . The fixed point "s" on this curve for the iteration "s = zetahurwitz(s, A324859)" is 0.5250984... .

Examples

			0.525098424628892572115438912395851316429631107548...
		

Crossrefs

Cf. A324859, A069857, A069995.

Programs

PARI

{ A324859 = solve(t = 1/16, 1/2, derivnum(x = t, solve(v = -1, 1 - x, v - zetahurwitz(v, x)), 2); ); solve(v = -1, 1 - A324859, v - zetahurwitz(v, A324859)) }