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A090986 Decimal expansion of Pi/sinh(Pi). 16
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Or, decimal expansion of Pi csch Pi.

Pi csch Pi = Prod[from n = 2 to infinity] (n^2 - 1)/(n^2 + 1). This is one of an infinite set of infinite products, the next being Prod[from n = 2 to infinity] (n^3 - 1)/(n^3 + 1) = 2/3. This is related to Ramanujan's surprising formula: Prod[from n = 1 to infinity] (prime(n)^2 - 1)/(prime(n)^2 + 1) = 5/2 and we use it in finding A112407 the semiprime analog. - Jonathan Vos Post, Dec 07 2005

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...

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

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. A114528-A114536.

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

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)