(537) 
the circle with M, as centre and A, M, as radius and symmetrically 
to the former the circle through 4, with radius Ms As, then we 
obtain for the region of convergence Gj a double segment, inside 
which lies the point z(P), where the mark of the series will be 
M, P: M, A, = M, P: My Az. 
Out of (VI) we find for function ¢an—! x the following series: 
tan—! EN 5 = nes ae (Gli "8 VE 
or 
en oe ee pea 
ele alah ea py Mn 
Who wishes to calculate tan—! L=> with the aid of this series 
will arrive at the best convergence for a=2, i.e. by placing M, in 
the point —z, and according to the above-mentioned the mark will 
be 1: 2. 
We shall find 
meel ah 
Ly PA ale SFO Ge 
+ glg—8 ety] talt— gts] + 
1rl 1 Weta eee ae 1 1 1 
ES eersel = ih tear ana ee — a Fs 35. | 
+315 oh ae ls ERD Arden 
Eri 1 1 1 1 
— | — = — 2S =| Se a: BN © 5 
R 3 hen zot 
