SOME RESULTS ON CYLINDRICAL CAVITY RESONATORS 



425 



which both reduce to Jf(kip) when c -^ 0. In the above, c is a parameter 

 related to the elHpticity.* The tables do not give values of the functions, 

 but rather give numerical coefficients 



Di and Fi 



of expansions in series of cosine, sine and Bessel functions, which permit one 

 to calculate the elliptic cylinder functions. The coefficients, of course, 



Fig. 6 — Elliptic coordinate system 



depend on the parameter c; the largest value of c in the tables is 4.5, which 

 corresponds to an ellipticity of 39% in a cylinder operating in the TE 01// 

 mode.** For this case, Bessel functions up to Jn(x) and Juix) are needed 

 for calculating the radial function. It is clear that calculations on elliptic 

 cylinders have not been put on a simple basis. 



* Not to be confused with c = velocity of electromagnetic waves; the symbol c is 

 here carried over from the published tables. 



** An ellipticity of 39% means that the difference between maximum and minimum 

 diameters is 39% of the maximum diameter. For a given c, the ellipticity depends oii 

 the mod^. 



