Converting a radial function to Cartesian form

[sergiomanzetti (Ser Man)]

Hi, I would like to convert the given function.

uA[r_, phi_] := {BesselJ[1.5 r, 5]*Exp[I 5 phi], 0 < r < 1/2};

to Cartesian form, but using

TransformedField["Polar" -> "Cartesian",  uA[r, phi], {r, phi} -> {x, y}]

I get something weird, which does not look like a function. It seems the boundary part 0<r<1/2 disturbs the conversion process and generates a wrong output. Is there a better way to do this?

Thanks

[mariuszi28cg (Mariusz Iwaniuk)]

Try:

 uA[r_, phi_] := BesselJ[3/2 r, 5]*Exp[I 5 phi]; TransformedField["Polar" -> "Cartesian", uA[r, phi], {r, phi} -> {x, y}]

 (*E^(5 I ArcTan[x, y]) BesselJ[3/2 Sqrt[x^2 + y^2], 5]*)

[sergiomanzetti (Ser Man)]

Thanks!