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%I #39 Jan 04 2023 15:40:42
%S 2,7,2,0,2,9,0,5,4,9,8,2,1,3,3,1,6,2,9,5,0,2,3,6,5,8,3,6,7,2,0,3,7,5,
%T 5,5,8,4,0,7,1,8,3,6,3,4,6,0,3,1,5,9,4,9,5,0,6,8,9,6,7,8,3,8,5,6,2,4,
%U 6,1,9,1,3,6,9,4,8,7,8,8,8,1,9,1,1,5,3,1,1,7,2,1,0,6,9,3,7,6,4,4,8,6,1,0
%N Decimal expansion of Pi/sinh(Pi).
%C Or, decimal expansion of Pi * csch(Pi).
%D Borwein, J.; Bailey, D.; and Girgensohn, R. "Two Products." Section 1.2 in Experimentation in Mathematics: Computational Paths to Discovery. Natick, MA: A. K. Peters, pp. 4-7, 2004.
%H G. C. Greubel, <a href="/A090986/b090986.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicCosecant.html">Hyperbolic Cosecant</a>.
%F Pi/sinh(Pi) = Prod_{k>=1} k^2/(k^2+1) = 0.27202905498213316295...
%F Pi * csch(Pi) = Product_{n >= 2} (n^2 - 1)/(n^2 + 1). - _Jonathan Vos Post_, Dec 07 2005
%F Equals Gamma(1+i)*Gamma(1-i), where i is the imaginary unit. - _Vaclav Kotesovec_, Dec 10 2015
%F Equals (1)_(-i)*(1)_i where (n)_k denotes the rising factorial. - _Peter Luschny_, May 06 2022
%F Equals 1 - 2*Sum_{n >= 1} (-1)^(n+1)/(n^2 + 1). - _Peter Bala_, Jan 01 2023
%e 0.272029054982133162950236583672...
%t Re[N[Gamma[1+I]*Gamma[1-I], 104]] (* _Vaclav Kotesovec_, Dec 09 2015 *)
%t RealDigits[Pi/Sinh[Pi],10,120][[1]] (* _Harvey P. Dale_, May 16 2019 *)
%o (PARI) default(realprecision, 100); Pi/sinh(Pi) \\ _G. C. Greubel_, Feb 02 2019
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/Sinh(Pi(R)); // _G. C. Greubel_, Feb 02 2019
%o (Sage) numerical_approx(pi/sinh(pi), digits=100) # _G. C. Greubel_, Feb 02 2019
%Y Cf. A112407, A144663 - A144669.
%K cons,nonn
%O 0,1
%A _Benoit Cloitre_, Feb 28 2004
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