Similar properties for the cylinder functions are 
Cita, bry) = — Cip(ery) a Ci41,46%Y) 
Ci pyg(tsy) = - Cy (ay) - - Op nace) 
2 
C 9 =-C 9 =— — 
10 (% 2) o1 (% 2) or 
C.. (x,y) C,, (2, y) - C,, (a, y) C (ay) ee 
00 MY) Oy MP 01 S79 Y) O49 UY mle) 
In the limit as 2 and y approach zero 
Dy (2a, ty) = oo Coo (ty) = - log # 
ix D, 9 («, ty) = ar tC (2,y) =1 
y Do, (tz, vy) = ins y Coy (t,y)=-1 
vy Diy (tx, cy) = a vy Cy (z, y) =0 
47 
