OFFSET
0,2
COMMENTS
G.f. yields asymptotic expansion of solutions to y''+(1+1/x)y=0.
REFERENCES
N. G. de Bruijn, Asymptotic Methods in Analysis, Dover, 1981, p. 197.
FORMULA
G.f. A(x)=y satisfies 16x^3y*y'+8x^4y*y''+y^4-12x^4y'^2-(1+4x)y^2=0.
PROG
(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))
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 27 2003
STATUS
approved