OFFSET
0,1
COMMENTS
LINKS
Daniel Duverney, Carsten Elsner, Masanobu Kaneko, and Yohei Tachiya, A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers, Research in Number Theory, Vol. 8 (2022), Article 31; alternative link.
Eric Weisstein's World of Mathematics, Dedekind Eta Function.
Wikipedia, Dedekind eta function.
FORMULA
EXAMPLE
0.33589766935710210314766572663122658048546104021373...
MATHEMATICA
With[{eta = DedekindEta, tau0 = Log[GoldenRatio]*I/Pi}, RealDigits[(Surd[GoldenRatio, 4] / Sqrt[5]) * eta[2*tau0]^2 * eta[6*tau0]/(eta[3*tau0] * eta[4*tau0]), 10, 120][[1]]]
PROG
(PARI) prodinf(k = 2, 1 - 1/(fibonacci(k-1) + fibonacci(k+1)))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 26 2024
STATUS
approved