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Search: id:A090986
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| A090986 |
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Decimal expansion of Pi/sinh(Pi). |
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+0
5
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (jvospost2(AT)yahoo.com), Dec 07 2005
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REFERENCES
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Infinite Product.
Eric Weisstein's World of Mathematics, Hyperbolic Cosecant
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FORMULA
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Pi/sinh(Pi) = prod(k>=1, k^2/(k^2+1)) = 0.27202905498213316295...
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EXAMPLE
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0.272029...
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CROSSREFS
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Cf. A114528-A114536.
Adjacent sequences: A090983 A090984 A090985 this_sequence A090987 A090988 A090989
Sequence in context: A125699 A060465 A139339 this_sequence A095194 A095711 A102886
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KEYWORD
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cons,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 28 2004
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