Fano limits again

I have long been an admirer of Harold Wheeler and his methodology; using these methods, Al Lopez has constructed an empirical closed-form solution (Equation (4) in A.R. Lopez (2005)) to the nonlinear simultaneous equations of Fano. The Lopez results agree to three significant figures with the exact solution of Fano´s equations (R.C. Hansen, 2005). Further, his augmented Tanner plot of the product of Q and bandwidth versus VSWR is quite useful. The confusion between Lopez and Hansen arose because the a_n and b_n coefficients of Fano are not the same as the a_n and b_n coefficients of Lopez