syms x k alpha
y=1;
fx=1/pi.^2/y.^(2./alpha).*2.^(alpha.*k).*(-1).^(k-1)./sym('k!').*(gamma(alpha.*k./2+1)).^2.*(sin(k.*alpha.*pi./2)).*(x./y.^(1./alpha)).^(-alpha.*k-2);
for N=1:8
fx_sum_1(N)= symsum(fx,k,1,N);
end
for N=1:8
fx_sum_subs_1= subs(fx_sum_1,{alpha},{1.1});% take the last term N.
end
fx_sum_subs_1(8);% use this term
rho=log(k.^2+x.^2);
rho_my=diff(rho,x);
fx_2=-0.0093*x^7+0.0745*x^6-0.2280*x^5+0.3000*x^4-0.0562*x^3-0.2156*x^2-0.0017*x+0.3072;
variance_my_3=(int(((rho_my.^2).*(fx_2)),x,0,2.2)+int(((rho_my.^2).*(fx_sum_subs_1(8))),x,2.2,inf))./((int(((diff(rho_my,x)).*fx_2),x,0,2.2)+(int(((diff(rho_my,x)).*fx_sum_subs_1(8)),x,2.2,inf))).^2);
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