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Search: id:A077230
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| A077230 |
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Numerators of coefficients of series expansion of a certain integral in the theory of charged particle beams. |
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+0
2
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| 2, 1, -7, 5, -787, 763, -893209, 2885597, -1153151299, 261937547, -3997632829, 30141297349, -4101190700056349, 2948796705108299, -320676905674696783, 43360062621189833, -5848606947453449297743, 1963629536423819469923, -575654781675816234791672323
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The integral is Integrate[1/Sqrt[Log[y]],{y,1,x}]=Sqrt[Pi]*Erfi[Sqrt[Log[x]] with series expansion Sqrt[x-1]*Sum[c(i)*(x-1)^(i-1),{i,0,19}]. Numerator(c(n))= A077230(n), denominator(c(n))=A077231(n).
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REFERENCES
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M. Reiser, Theory and design of charged particle beams. J. Wiley, N.Y. 1994, S. Humphries, Charged particle beams. J. Wiley, N.Y. 1990.
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EXAMPLE
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Series expansion is Sqrt[x-1]*(2 + 1/6 (x-1) -7/240 (x-1)^2+ 5/448 (x-1)^3 -...), hence a(0)=2, a(1)=1, a(2)=-7, a(3)=5, etc.
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CROSSREFS
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Cf. A077231.
Sequence in context: A124821 A104030 A082791 this_sequence A019668 A091700 A157743
Adjacent sequences: A077227 A077228 A077229 this_sequence A077231 A077232 A077233
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KEYWORD
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sign,frac
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2002
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