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%I #15 Aug 06 2024 06:14:24
%S 1,0,0,0,0,0,0,0,0,0,0,7,6,1,2,2,6,9,3,8,4,8,9,9,2,6,7,3,8,4,3,7,2,8,
%T 4,5,1,1,3,3,4,5,0,7,3,6,2,7,3,3,8,8,1,9,4,6,6,3,9,3,6,6,9,1,7,7,1,5,
%U 4,9,7,2,3,0,8,9,6,3,4,0,9,5,3,7,8,7,3
%N Decimal expansion of (1 + sqrt(3 + 2*sqrt(5)))/sqrt(2) * exp(-Pi*sqrt(55)/24).
%C Ramanujan's question 489 in the Journal of the Indian Mathematical Society (V, 200) asked "Show that (1 + exp(-Pi*sqrt(55))) * (1 + exp(-3*Pi*sqrt(55))) * (1 + exp(-5*Pi*sqrt(55))) ... = (1 + sqrt(3 + 2*sqrt(5)))/sqrt(2) * exp(-Pi*sqrt(55)/24)."
%H B. C. Berndt, Y. S. Choi, and S. Y. Kang, <a href="https://faculty.math.illinois.edu/~berndt/jims.ps">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q489, JIMS V).
%H B. C. Berndt, Y. S. Choi, and S. Y. Kang, <a href="https://citeseerx.ist.psu.edu/pdf/ae75da0be9fb455e2c55daa5fca46ae63e6a60bd">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q489, JIMS V).
%e 1.00000000007612269384899267384372845113345073627338819466393669...
%t RealDigits[(1 + Sqrt[3+2*Sqrt[5]])/Sqrt[2] * Exp[-Pi*Sqrt[55]/24], 10, 120][[1]] (* _Amiram Eldar_, Jun 27 2023 *)
%o (PARI) (1+sqrt(3+2*sqrt(5)))/sqrt(2)*exp(-Pi*sqrt(55)/24)
%o (PARI) prodinf(k=0,(1+exp(-Pi*sqrt(55))^(2*k+1)))
%K nonn,cons,changed
%O 1,12
%A _Hugo Pfoertner_, Sep 18 2018
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