A090986 Decimal expansion of Pi/sinh(Pi).

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, 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, 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

Offset

0,1

Comments

Or, decimal expansion of Pi * csch(Pi).

References

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Infinite Product.

Eric Weisstein's World of Mathematics, Hyperbolic Cosecant.

Formula

Pi/sinh(Pi) = Prod_{k>=1} k^2/(k^2+1) = 0.27202905498213316295...

Pi * csch(Pi) = Product_{n >= 2} (n^2 - 1)/(n^2 + 1). - Jonathan Vos Post, Dec 07 2005

Equals Gamma(1+i)*Gamma(1-i), where i is the imaginary unit. - Vaclav Kotesovec, Dec 10 2015

Equals (1)_(-i)*(1)_i where (n)_k denotes the rising factorial. - Peter Luschny, May 06 2022

Equals 1 - 2*Sum_{n >= 1} (-1)^(n+1)/(n^2 + 1). - Peter Bala, Jan 01 2023

Example

0.272029054982133162950236583672...

Mathematica

Re[N[Gamma[1+I]*Gamma[1-I], 104]] (* Vaclav Kotesovec, Dec 09 2015 *)
RealDigits[Pi/Sinh[Pi], 10, 120][[1]] (* Harvey P. Dale, May 16 2019 *)

Prog

(PARI) default(realprecision, 100);  Pi/sinh(Pi) \\ G. C. Greubel, Feb 02 2019
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/Sinh(Pi(R)); // G. C. Greubel, Feb 02 2019
(Sage) numerical_approx(pi/sinh(pi), digits=100) # G. C. Greubel, Feb 02 2019

Crossrefs

Cf. A112407, A144663 - A144669.

Sequence in context: A060465 A219177 A139339 * A245221 A195726 A095194

Adjacent sequences: A090983 A090984 A090985 * A090987 A090988 A090989

Keyword

cons,nonn

Author

Benoit Cloitre, Feb 28 2004

Status

approved