**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)