@Carl Love Hi Carl, I have attached my whole worksheet. I assume it can be accessed?

@Carl Love 

Hi sorry! Im getting a little mixed up....

I have values of E which I have as Y

and values of f which I have as X

I want the parameters a, b, c and d given the equation is satified by the corresponding E and f (Y and X) values?

@rlopez 

I have attached what I have so far although it seems very wrong considering my Y values are effiecincies 

Download Detectors_Tutorial.mw

@Preben Alsholm 

f:= HankelH1(2, z);

appologies I thought I had included all of the code 

@Just_Some_Guy 

z_max := 50+10*I; z_min := -50-10*I; step := .2+.2*I;
i_max := (z_max-z_min)/step;
j := 1;
for i from 0 to 10 do z0 := i*step+z_min; x[j] := fsolve(f = 0, z = z0, complex) end do;
for p to 10 do for j from p+1 to 9 do if `and`(Re(x[j])-Re(x[p]) < 0.1e-4, Im(x[j])-Im(x[p]) < 0.1e-4) then for i from j to 10 do x[i] := x[i+1] end do; p := p-1; break end if end do end do;

@Preben Alsholm 

z_max := 50+10*I; z_min := -50-10*I; step := .2+.2*I; 50 + 10 I

-50 - 10 I
0.2 + 0.2 I
i_max := (z_max-z_min)/step;
j := 1;
for i from 0 to 10 do z0 := i*step+z_min; x[j] := fsolve(f = 0, z = z0, complex) end do;
for p to 10 do for j from p+1 to 9 do if `and`(Re(x[j])-Re(x[p]) < 0.1e-4, Im(x[j])-Im(x[p]) < 0.1e-4) then for i from j to 10 do x[i] := x[i+1] end do; p := p-1; break end if end do end do;

@Kitonum is there any way to do it with the already given program? I'm trying to do it step by step?

thanks for your answer