Question: how to get a polynomial with degree n?

i calculate a polynomial as following

yn := f(x) = _C1*hypergeom([-(1/2)*n, 3/2+(1/2)*n], [1/2], x^2)+_C2*hypergeom([2+(1/2)*n, 1/2-(1/2)*n], [3/2], x^2)*x


want to get the polynomial with degree n  for  summation_n_from_0_to_infinity y_n*z^n/n!

such as n = 1 n = 0 n = 3, but above yn is hypergeom, is n represent degree, if so, i use subs, then is finished, if not, how to get polynomial with degree n?

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