OFFSET
1,3
COMMENTS
The second part of Ramanujan's question 352 in the Journal of the Indian Mathematical Society (IV, 40) asked "Show that 1 / (1 - exp(-Pi) / (1 + exp(-2*Pi) / (1 - exp(-3*Pi) / (1 + ...)))) = (sqrt((5 - sqrt(5))/2) - (sqrt(5) - 1)/2) * exp(Pi/5)". Also stated in Ramanujan's first letter to G. H. Hardy in 1913. Corrected version from page 28 of Berndt, Choi and Kang, see links.
LINKS
B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q352, JIMS IV).
B. C. Berndt, Y. S. Choi, S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q352, JIMS IV).
EXAMPLE
1.045077716158131508243004427816406605231289465608379931518029618...
MATHEMATICA
First[RealDigits[(Sqrt[(5 - Sqrt[5])/2] - GoldenRatio + 1)*Exp[Pi/5], 10, 100]] (* Paolo Xausa, Apr 27 2024 *)
PROG
(PARI) (sqrt((1/2)*(5-sqrt(5)))-(sqrt(5)-1)/2)*exp(Pi/5)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Sep 16 2018
STATUS
approved