234 
a) n= even q = 9 +» De, ae | 
: LEM 
Ys == in Ps = Pn 
Fs — Qnl Ps — Pul 
q; — qn-2 Ps = Pn—2 
(14a) 
ae Ten er Deden 
—= 42 Ent Et 
dei a1 LM 
rm \ iS -—? 
b) n’ = odd q, =e Pr en sy 
da — ‘Gn! P2 = Pn’ 
qs = Inl Ps =pri-1—_¢ (148) 
eons =S ij : Ee ee pee re! 
Thus we find, when even or odd, values of the p’s which 
two and two are equal. 
Now, calculating in the same way as in| the roots of (10), we find 
for n = even az = (-—1)F Ccos (4 n—k) O 
for n’ = odd a’, = (—1)¥ C sin (4 n’—hk) 9 
where U is an arbitrary constant. 
Considering the @’s, we can easily see the equalities form = even 
a, == At 
a, — an—2 
ai —— 
Si —1 as 
and for the remaining «@, and @,, 
1 
a, =(—1)2" Ceos 0 
fl 
2 
and 
ay = Ces 4 10 
In the same way, we find for », = odd, 
a, — Ci’ —1 
ai 1—41 1 
, rts pel 
at Santis 
