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Search: id:A122214
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| A122214 |
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Numerators in infinite products for Pi/2, e and e^gamma (reduced). |
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+0
6
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| 1, 2, 4, 32, 4096, 67108864, 4503599627370496, 2535301200456458802993406410752, 4084620902943761579745625423246687265522976897405582347410338578593480704
(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) = numerator(product(k = 1...n, k^((-1)^k*binomial(n-1,k-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 A122215. Unreduced numerators are A122216.
Sequence in context: A101460 A118992 A062740 this_sequence A122216 A100117 A073888
Adjacent sequences: A122211 A122212 A122213 this_sequence A122215 A122216 A122217
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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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