New Approximations of Feigenbaum Constants

Feig1 = 4.669201609... = First Feigenbaum Constant (\delta, or \delta_2)

Feig2 = 2.502907875…= Second Feigenbaum Constant (\alpha, or \alpha_2)

1.9276909638… = | \alpha_3 |

4.669201656... = Pi + ArcCos[3 Exp[-Pi] Log[2]^3]

(abs) err < 5 E-8 (with respect to Feig1)

4.66919… = Tan[2/3+Log[2]]

(abs) err < 1 E-5 (with respect to Feig1)

1.9276925…=(1+Exp[EulerGamma])Log[2]

(abs) err <2 E-6 (with respect to alpha_3)

An approximate relation between First and Second Feigenbaum Constants:

4.669206… = Pi ArcTan[4Exp[alpha]/(1+Pi)]

or

Pi ArcTan[4Exp[Feig2]/(1+Pi)] - Feig1 < 5 E-6

Alessandro Soranzo (2015)