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Search: id:A077231
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| A077231 |
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Denominators 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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| 1, 6, 240, 448, 138240, 225280, 402554880, 1857945600, 1010722406400, 301234913280, 5859811786752, 55010477998080, 9141306387333120000, 7898088718655815680, 1017975879293416243200, 161212016644168089600
(list; graph; listen)
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OFFSET
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0,2
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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)=1, a(1)=6, a(2)=240, a(3)=448, etc.
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CROSSREFS
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Cf. A077230.
Sequence in context: A099124 A099129 A145180 this_sequence A002022 A065948 A052510
Adjacent sequences: A077228 A077229 A077230 this_sequence A077232 A077233 A077234
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KEYWORD
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frac,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 31 2002
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