OFFSET
1,1
COMMENTS
This constant is transcendental (Duverney et al., 1998).
REFERENCES
Daniel Duverney, Keiji Nishioka, Kumiko Nishioka, and Iekata Shiokawa, Transcendence of Jacobi's theta series and related results, in: K. Györy, et al. (eds.), Number Theory, Diophantine, Computational and Algebraic Aspects, Proceedings of the International Conference held in Eger, Hungary, July 29-August 2, 1996, de Gruyter, 1998, pp. 157-168.
LINKS
Daniel Duverney and Iekata Shiokawa, On series involving Fibonacci and Lucas numbers I, AIP Conference Proceedings, Vol. 976, No. 1. American Institute of Physics, 2008, pp. 62-76.
Derek Jennings, On reciprocals of Fibonacci and Lucas numbers, Fibonacci Quarterly, Vol. 32, No. 1 (1994), pp. 18-21.
Eric Weisstein's World of Mathematics, Jacobi Theta Functions.
FORMULA
EXAMPLE
2.39741418791652120040922449568177870852072229637554...
MATHEMATICA
RealDigits[Sum[k/Fibonacci[2*k], {k, 1, 300}], 10, 100][[1]]
PROG
(PARI) sumpos(k=1, k/fibonacci(2*k)) \\ Michel Marcus, Sep 10 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Sep 10 2022
STATUS
approved