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 A318739 Decimal expansion of Pi^2 / 24 - (1/12) * log(2 + sqrt(5))^2. 0

%I

%S 2,3,7,5,5,9,9,0,1,2,7,9,1,6,0,8,1,4,7,4,5,4,0,6,9,8,8,2,3,7,8,5,6,7,

%T 2,7,2,9,2,4,3,2,7,1,2,7,6,4,7,2,5,4,5,6,3,2,2,4,1,3,6,3,5,8,2,5,1,5,

%U 5,3,5,8,4,2,5,5,7,8,8,5,8,7,1,9,6,1

%N Decimal expansion of Pi^2 / 24 - (1/12) * log(2 + sqrt(5))^2.

%C Ramanujan's question 606 in the Journal of the Indian Mathematical Society (VI, 239) asked "Show that Sum_{n>=0} (sqrt(5) - 2)^(2*n + 1) / (2*n + 1)^2 = Pi^2/24 - (1/12) * (log(2 + sqrt(5)))^2".

%H B. C. Berndt, Y. S. Choi, 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 Q606, JIMS VI).

%H B. C. Berndt, Y. S. Choi, S. Y. Kang, <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.9228">The problems submitted by Ramanujan to the Journal of Indian Math. Soc.</a>, in: Continued fractions, Contemporary Math., 236 (1999), 15-56 (see Q606, JIMS VI).

%e 0.2375599012791608147454069882378567272924327127647254563224136358251...

%o (PARI) Pi^2/24-(1/12)*log(2+sqrt(5))^2

%o (PARI) suminf(k=0,(sqrt(5)-2)^(2*k+1)/(2*k+1)^2)

%K nonn,cons

%O 0,1

%A _Hugo Pfoertner_, Sep 16 2018

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)