A102817 Decimal expansion of Gamma(delta)^2 where delta is the Feigenbaum bifurcation velocity constant (A006890).

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

Offset: 3

Author

Gerald McGarvey, Feb 26 2005

Keywords

• cons
• nonn

Comments

Let x be this constant, then Integral_{t=1..x} sin(t)/sqrt(t) dt = 0.655555692248871113068...

delta^2 = 21.8014436664499573..., (delta/Gamma(delta))^2 = 0.10000663312663433933000349...

If s is solution of Gamma(s) - sqrt(218) = 0 then 1/((s - delta)*Gamma(delta)^6) = 2.5555951358396... whereas a^(Pi/4) = 2.055596478435... where a is Feigenbaum alpha constant (A006891), the difference = 0.4999986574... ~ 1/(2 + 10^-5.27)

10*cos(Gamma(delta)^2) + Pi = -0.199999019922688714710053...

Examples

			217.99997644999881468628813957793609890726797890973...
		

Links

• D. Broadhurst, Feigenbaum constants to 1018 decimal places

Crossrefs

Cf. A006890, A006891.

Programs

Mathematica

Set delta then RealDigits[Gamma[delta]^2, 10, 110][[1]]

PARI

acos(Pi/10+.0199999019922688714710053)+69*Pi \\ Yields ~ 30 digits. Using (2e5-1)/(1e7-1) yields ~ 15 digits. For a better value use, e.g., delta from the Broadhurst link. - M. F. Hasler, Apr 30 2018