Mutual Induction. 367 
Again, if F( , /2) ^_,^, 
but it can be shown that 
-P/+(r+l)P,= P^i. 
FW)=--2-^ P '-.. 
and 
^^. — [(.r+sye^+f.^] 
1 1 „,, 
since ^P/ + (r-+l)P,=P; +l . 
P 
^P/'-K.r + 2)P/=P;' +1 , 
P 
or ?-'pi' + i + (r+3)P^i^P2«- 
P 
F .(j'«)=(-i)'i . j^i+iP^.-- 
where p« Ws (A) s p W . 
But 
(i)'(»)'0H-^[^~-^ ■ ^•^.-■■] 
Finally if A — A' is small 
2C2 
