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Search: id:A122216
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| A122216 |
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Numerators in infinite products for Pi/2, e and e^gamma (unreduced). |
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6
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| 1, 2, 4, 32, 4096, 201326592, 3283124128353091584, 26520146032764463901929624736590416838656, 8409872218845584878346591802015832570333859884111674529900728420499238460920
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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J. Sondow, A faster product for Pi and a new integral for ln Pi/2, Amer. Math. Monthly 112 (2005) 729-734.
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LINKS
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J. Baez, This Week's Finds in Mathematical Physics
J. Guillera and J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
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FORMULA
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a(n) = product(k = 1...ceiling(n/2), (2k)^binomial(n,2k-1)).
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EXAMPLE
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Pi/2 = (2/1)^(1/2) * (4/3)^(1/4) * (32/27)^(1/8) *
(4096/3645)^(1/16) * ...,
e = (2/1)^(1/1) * (4/3)^(1/2) * (32/27)^(1/3) * (4096/3645)^(1/4) * ... and
e^gamma = (2/1)^(1/2) * (4/3)^(1/3) * (32/27)^(1/4) * (4096/3645)^(1/5) *
....
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CROSSREFS
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Cf. A092798. Denominators are A122217. Reduced numerators are A122214.
Sequence in context: A118992 A062740 A122214 this_sequence A100117 A073888 A114642
Adjacent sequences: A122213 A122214 A122215 this_sequence A122217 A122218 A122219
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KEYWORD
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frac,nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 26 2006
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