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Search: id:A087220
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| A087220 |
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Coefficients in an asymptotic series expanded in powers of 1/(4x). |
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+0
1
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| 1, 2, -2, -12, 126, -84, -10532, 72584, 1398454, -23934644, -279791836, 10005551128, 74538179116, -5628788533000, -20339727800264, 4187789575589776, -1855072071151834, -4010464443848609780
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OFFSET
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0,2
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COMMENT
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G.f. yields asymptotic expansion of solutions to y''+(1+1/x)y=0.
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REFERENCES
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N. G. de Bruijn, Asymptotic Methods in Analysis, Dover, 1981, p. 197.
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FORMULA
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G.f. A(x)=y satisfies 16x^3y*y'+8x^4y*y''+y^4-12x^4y'^2-(1+4x)y^2=0.
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PROGRAM
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(PARI) a(n)=local(A, A1); if(n<0, 0, A=1+2*x+O(x^2); for(k=1, n\2, A1=x^2*A'; A=sqrt((1+4*x)/(1+(8*x^2*A1'*A-12*A1^2)/A^4))); polcoeff(A, n))
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CROSSREFS
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Sequence in context: A032321 A013311 A136278 this_sequence A032320 A032227 A032069
Adjacent sequences: A087217 A087218 A087219 this_sequence A087221 A087222 A087223
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 27 2003
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