Question: seriestoratpoly error

Question:seriestoratpoly error

Ex 85 Maple

opoly := (1-x^2)*diff(f(x), x$2) - x*diff(f(x), x) + n^2*f(x) = 0;
sol := op(2,dsolve(opoly));
gen := sum(cos(n*arcsin(x))*y^n/n!, n=0..7);

with(gfun):
seriestoratpoly(series(gen, z, 8), ['egf']);

error not a series, why?


seriestoratpoly(gen, ['egf']);

refere to the following link, it is possible to use a few terms to calculate a generating function, but where is the function generating? how do it  work in gfun?

http://www.google.com.hk/url?sa=t&source=web&cd=2&ved=0CCEQFjAB&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.66.4690%26rep%3Drep1%26type%3Dpdf&rct=j&q=maple%20convert%20series%20into%20generating%20function&ei=FceDTuXZC4aUiAfco9T3Dg&usg=AFQjCNFeJfH5zSurQOk7jG-8ZVkj4f0ePA&cad=rja

 

use infinity different from the result in http://www.solitaryroad.com/c682.html

gen := sum(cos(n*arcsin(x))*y^n/n!, n=0..infinity);

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