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Search: id:A122215
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| A122215 |
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Denominators in infinite products for Pi/2, e and e^gamma (reduced). |
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+0
5
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| 1, 1, 3, 27, 3645, 61509375, 4204742431640625, 2396825584582984447479248046875, 3896237517467890187050354408614984136338676989907980896532535552978515625
(list; graph; listen)
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OFFSET
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1,3
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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) = denominator(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. A092799. Numerators are A122214. Unreduced denominators are A122217.
Sequence in context: A078233 A009039 A137092 this_sequence A122217 A068221 A068222
Adjacent sequences: A122212 A122213 A122214 this_sequence A122216 A122217 A122218
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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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