Some New Approximations of Feigenbaum Constants 1 Introduction

Some New Approximations of Feigenbaum Constants
Alessandro SORANZO
Dipartimento di Matematica e Geoscienze
Università degli Studi di Trieste - Trieste - Italy
On the net: 31 March 2016 – Last updated: 31 March 2016
Keywords: Feigenbaum Constants
1
Introduction
Let’s remember theese numerical values of the First Feigenbaum Constant,
Second Feigenbaum Constant and Euler’s Gamma:
δ = 4.669201609102990671853203820466201617258185577 · · ·
α = 2.5029078750958928222839028732182157863812713767271 · · ·
γ = 0.577215664901532860606512090082402431042159335939 · · ·
Let’s denote by ε the absolute error and by εr the relative error.
2
α '
1 '
New Approximations
e1/e
γ
q
= 2.502822 · · ·
δ arctan α /α2 = 0.999933 · · ·
|ε| < 9 · 10−5
|ε| < 7 · 10−5