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How can I derive the inverse z-transform of:

$\sqrt{\frac{1-a^2}{1-\frac{a}{z}}}$

If Maple is not the way, how to derive manually?

With Maple code I encounter some problems

seriestoratpoly(series(simplify(LaguerreL(5, a, x)),x,6),['egf']);  restart; alpha := 0; s := x; tau := alpha + 1 - x; source := s*Diff(y(x),x$2)+tau*Diff(y(x),x)+n*y(x)=0; sol := dsolve(source,y(x),method=laplace); zsol := ztrans(sol,x,z); convert(zsol, ratpoly);  sol := y(x) = _C1*invlaplace((_s1-1)^n*_s1^(-1-n), _s1, x) zsol := ztrans(y(x), x, z) = _C1*invlaplace((_s1-1)^n*_s1^(-1-n)*z/(z-1), _s1, x) Error, (in convert/ratpoly) expecting a Laurent series or a Chebyshev series  what are _C1 and _s1?   > with(gfun); ratp := seriestoratpoly(dsolve(source, y(x), series), ['egf']); Error, (in gfun:-seriestoratpoly) not a series, y(x) = _C1*(series(1-n*x+((1/4)*(n-1)*n)*x^2-((1/36)*(-2+n)*(n-1)*n)*x^3+((1/576)*(-3+n)*(-2+n)*(n-1)*n)*x^4-((1/14400)*(n-4)*(-3+n)*(-2+n)*(n-1)*n)*x^5+O(x^6),x,6))+_C2*(ln(x)*(series(1-n*x+((1/4)*(n-1)*n)*x^2-((1/36)*(-2+n)*(n-1)*n)*x^3+((1/576)*(-3+n)*(-2+n)*(n-1)*n)*x^4-((1/14400)*(n-4)*(-3+n)*(-2+n)*(n-1)*n)*x^5+O(x^6),x,6))+(series((1+2*n)*x+(-(1/2)*n+1/4-(3/4)*(n-1)*n)*x^2+((1/36)*(n-1)*n+(1/36)*(-2+n)*n+(1/36)*(-2+n)*(n-1)+(11/108)*(-2+n)*(n-1)*n)*x^3+(-(1/576)*(-2+n)*(n-1)*n-(1/576)*(-3+n)*(n-1)*n-(1/576)*(-3+n)*(-2+n)*n-(1/576)*(-3+n)*(-2+n)*(n-1)-(25/3456)*(-3+n)*(-2+n)*(n-1)*n)*x^4+...  do not know _C1 and _C2 if assume _C1 and _C2 = 1  with(gfun); ratp := seriestoratpoly(subs(_C1=1,subs(_C2=1,dsolve(source, y(x), series))), ['egf']); output FAILED 
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