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Search: id:A078791
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| A078791 |
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Expansion of Auxiliary function L(m_1)/4 in powers of m/16. |
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1
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| 0, 1, 21, 740, 37310, 2460024, 200770416, 19551774528, 2213488134000, 285711909912000, 41419784380740480, 6663725042739448320, 1178209566488368028160, 227096910697908706560000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Nome q(m) = x exp(8(Sum_{n>0} a(n)x^n/n!)/(Sum_{n>=0} binomial(2n,n)^2 x^n)) where x=m/16.
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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 9.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 591.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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E.g.f.: L(m_1)= K(m)/pi log(16/m)-K(m_1)= 4 Sum_{n>0}a(n)(m/16)^n/n!.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sum(k=1, n, 1/(2*k-1)/k)/4*(2*n)!^2/n!^3)
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CROSSREFS
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Cf. A005797.
Sequence in context: A056565 A009167 A012479 this_sequence A143002 A062755 A012850
Adjacent sequences: A078788 A078789 A078790 this_sequence A078792 A078793 A078794
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Dec 05, 2002
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