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Decimal expansion of c = Product_{k>=1} (1 + 1/k^2)^2.
1

%I #20 Jan 04 2021 13:55:02

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

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

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

%N Decimal expansion of c = Product_{k>=1} (1 + 1/k^2)^2.

%D Bruce C. Berndt, Ramanujan Notebook part II, Integral and asymptotic expansions, Springer Verlag, p. 230, entry 27.

%F Equals (cosh(2*Pi)-1)/(2*Pi^2).

%F Equals (sinh(Pi)/Pi)^2. - _Bernard Schott_, Jan 04 2021

%e 13.513548803146862731723815...

%t Sinh[Pi]^2/Pi^2 // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Mar 04 2013 *)

%o (PARI) (cosh(2*Pi)-1)/2/Pi^2

%K cons,nonn

%O 2,2

%A _Benoit Cloitre_, Jun 21 2003