OFFSET
0,1
COMMENTS
Or, decimal expansion of Pi * csch(Pi).
REFERENCES
Jonathan M. Borwein, David H. Bailey, and Roland Girgensohn, "Two Products", Section 1.2 in Experimentation in Mathematics: Computational Paths to Discovery, Natick, MA: A. K. Peters, 2004, pp. 4-7.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Hyperbolic Cosecant.
Eric Weisstein's World of Mathematics, Infinite Product.
FORMULA
Equals Pi/sinh(Pi) = Product_{k>=1} k^2/(k^2+1).
Equals 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
Equals A212879^2. - Amiram Eldar, Oct 25 2024
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
KEYWORD
AUTHOR
Benoit Cloitre, Feb 28 2004
STATUS
approved