|
| |
|
|
A090986
|
|
Decimal expansion of Pi/sinh(Pi).
|
|
12
| |
|
|
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; 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 (jvospost3(AT)gmail.com), 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
| 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...
|
|
|
EXAMPLE
| 0.272029054982133162950236583672...
|
|
|
CROSSREFS
| Cf. A114528-A114536.
Sequence in context: A125699 A060465 A139339 * A195726 A095194 A095711
Adjacent sequences: A090983 A090984 A090985 * A090987 A090988 A090989
|
|
|
KEYWORD
| cons,nonn
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 28 2004
|
| |
|
|
