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A092563
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Coefficients in asymptotic expansion of I_0(x)sqrt(2*pi*x)/e^x in powers of 1/(16x).
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0
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1, 2, 18, 300, 7350, 238140, 9604980, 463783320, 26087811750, 1675417243500, 120965124980700, 9699203657543400, 855146455806743100, 82225620750648375000, 8563211075317523625000, 960221401912271649150000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| F. Bowman, Introduction to Bessel functions, Dover Publications Inc., New York 1958, see page 48. MR0097539
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 377. 9.7.1
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LINKS
| 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
| E.g.f. A(x)=y satisfies (8x^2-x)y''+(16x-1)y+2y=0. G.f. A(x)=y satisfies 8x^2y''+(16x-1)y+2y=0.
E.g.f.: F(1/2, 1/2;1;8x) = 1/AGM(1, (1-8x)^(1/2)). a(n)=(2n)!^2/(n!^3 2^n).
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EXAMPLE
| I_0(x)sqrt(2*pi*x)/e^x ~ 1+2/(16x)+18/(16x)^2+300/(16x)^3+... where I_0(x) is a Bessel function
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PROG
| (PARI) a(n)=if(n<0, 0, (2*n)!^2/n!^3/2^n)
(PARI) a(n)=if(n<0, 0, n!*polcoeff(1/agm(1, sqrt(1-8*x+x*O(x^n))), n))
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CROSSREFS
| a(n)2^n=A002894(n)n!.
Sequence in context: A084947 A123385 A121564 * A192555 A179497 A087215
Adjacent sequences: A092560 A092561 A092562 * A092564 A092565 A092566
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Feb 28 2004
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