Dear Robert, thank you very much for your kind help.  I really like Maple, it is a powerful programme.  Yes I recognized that rootfinding doesn't like CylinderD functions as you said, it gives error messages about the first derivative of them. Now I would like to study my main complicated and long complex equation(which is in terms of CylinderD(n,z) and CylinderD(n, I*z),  functions) and tried to find the real zeros..

Dear Robert, thank you very much for your kind help.  I really like Maple, it is a powerful programme.  Yes I recognized that rootfinding doesn't like CylinderD functions as you said, it gives error messages about the first derivative of them. Now I would like to study my main complicated and long complex equation(which is in terms of CylinderD(n,z) and CylinderD(n, I*z),  functions) and tried to find the real zeros..

Dear Hirnyk, I appreciated your help, thank you.

Dear Hirnyk, I appreciated your help, thank you.

Dear Axel, thank you very much for your kind help. i really appreciated it.

Dear Axel, thank you very much for your kind help. i really appreciated it.

Hi, thank you very much for your reply. Yes I agree with you. In fact my equation is more complicated and too long, I would like to give this CylinderD(n,2)*CylinderD(n,2*I)+exp(I*n*Pi/2); as an example.  But I didn`t know that I could use plots[complexplot] here. On the other hand, there is an equation and one claims that he obtained the real roots of this equation:

V:=1.0; z:=2.0; W:=(2^(n+3/2)*Pi)/(GAMMA(-n/2)*GAMMA(1/2-n/2));

and

1+((abs(V))^2/W^2)*(CylinderD(n,z)^2)*(CylinderD(n,-z)^2-CylinderD(n,z)^2)=0.

He gets n=0.056, 1.28, 1.92, ...etc

But for V=10.0 he gets both real and complex conjugate roots. I tried to get this result by Maple but I couldn`t obtain it. Some maple commands such as with(RootFinding) doesn`t work for the Cylinder functions. I should be wrong maybe.

Hi, thank you very much for your reply. Yes I agree with you. In fact my equation is more complicated and too long, I would like to give this CylinderD(n,2)*CylinderD(n,2*I)+exp(I*n*Pi/2); as an example.  But I didn`t know that I could use plots[complexplot] here. On the other hand, there is an equation and one claims that he obtained the real roots of this equation:

V:=1.0; z:=2.0; W:=(2^(n+3/2)*Pi)/(GAMMA(-n/2)*GAMMA(1/2-n/2));

and

1+((abs(V))^2/W^2)*(CylinderD(n,z)^2)*(CylinderD(n,-z)^2-CylinderD(n,z)^2)=0.

He gets n=0.056, 1.28, 1.92, ...etc

But for V=10.0 he gets both real and complex conjugate roots. I tried to get this result by Maple but I couldn`t obtain it. Some maple commands such as with(RootFinding) doesn`t work for the Cylinder functions. I should be wrong maybe.