do maple have tree data structure for genetic programming?

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&...

opoly := (1-x^2)*diff(f(x), x$2) - x*diff(f(x), x) + n^2*f(x) = 0;
sol := op(2,dsolve(opoly));
P := sum(cos(n*arcsin(x))*z^n/n!, n=0..7);
with(gfun):
algeqtoseries(P, x, z, 7, true);

Error, invalid input: gfun:-algeqtoseries expects its 1st argument, Pol, to be of type polynom(anything, [x, y]), but received 1+(1-x^2)^(1/2)*z+(1/2)*cos(2*arcsin(x))*z^2+(1/6)*cos(3*arcsin(x))*z^3+(1/24)*cos(4*arcsin(x))*z^4+(1/120)*cos(5*arcsin(x))*z^5+(1/720)*cos(6*arcsin(x))*z^6+(1/5040)*cos(7*arcsin(x))*z^7...

http://www.solitaryroad.com/c681.html

refer to this link, dsolve the differential equation can not get generating function.

would you mind demonstrating the steps with maple?

1. can it have simple solution for convert(taylor(Qx*exp(z), z=0,5), ratpoly); as my solution have     hypergeom([-1/2i, ....?

    for example where Qx = x/m, if m is also increasing from 0 to 5 by one in each term

    How to write these command?

    is it sum(Qx*z^m/m!, m=0..infinity); but convert this result to ratpoly result in error, if exp, it will have summation,