A077231 Denominators of coefficients of series expansion of a certain integral in the theory of charged particle beams.

1, 6, 240, 448, 138240, 225280, 402554880, 1857945600, 1010722406400, 301234913280, 5859811786752, 55010477998080, 9141306387333120000, 7898088718655815680, 1017975879293416243200, 161212016644168089600

Offset

0,2

Comments

The integral is Integral_{y=1..x} 1/sqrt(log(y)) dy = sqrt(Pi)*Erfi(sqrt(log(x))) with series expansion sqrt(x-1)*Sum_{i>=0} c(i)*(x-1)^i.

Numerator(c(n)) = A077230(n), denominator(c(n)) = A077231(n).

References

M. Reiser, Theory and design of charged particle beams. J. Wiley, N.Y. 1994, S. Humphries, Charged particle beams. J. Wiley, N.Y. 1990.

Links

Table of n, a(n) for n=0..15.

Example

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.

Crossrefs

Cf. A077230 (numerators).

Sequence in context: A397244 A256275 A235346 * A172965 A002022 A378778

Adjacent sequences: A077228 A077229 A077230 * A077232 A077233 A077234

Keyword

frac,nonn

Author

Zak Seidov, Oct 31 2002

Status

approved