304 
After calculation of the numerators (to which also P, has been 
added), we have: 
Perey at 1 Aesha a! 1 
(24 fed ke —: ; P Te 8 — = 
1 (2 a’) ‘ls th 3 (?—a?)'*I2 | 
) 3 
Pp = Ll +157 [4q?+-*°/,J?a*+*/,,a° 1 f | ( ) 
. (U —a?)"ls derd ern a 
For small values of z F': e? approaches: 
At 
(z=0) F':e =AP oc t8P et +12P,e' + etc. ; vels 7 +0) (4) 
Remark. That the coefficients of /?, /*, /°, ete. in the expressions 
for P,, P,, P,, etc. become every time =1, is not surprising. For 
1.3 jee 1.3.5.7 sags Tee Ae 
they are resp. (7) +5) re (reel + 2 (5: zie) Ha) ‘ 
etc., being the coefficients of the expansion of (l—y)"/: (1—y) hz, 
ie. of (1—y)—1, which are all —1. The coefficients of a’, a‘, a’ etc., 
viz. 1/5, */e> °/‚ etc. are evidently those of the expansion (/=0) 
Zev kh zei ge \H ist oe A 13.44.35 
of (1—=) (1+) =(1-5) Je DEL 946° ete: 
According to what follows, the coefficients of the second terms, viz. 
ty, 0) A4, etc. are represented for!P, Pie. 2, by */,n( Jd 
1542 34-7 KS 
ber = en, ‚ etc. | When we add to this resp. */,, °/,, 
etc. (=1/,(2n-+ 3)) of the exponents in the denominators, we get 
the coefficients of the limiting values of P,, P,, etc. for /=o, 
34 9X6 XB 
mentioned farther on viz. '/, (n + 2) (n + 3) = 5 ; : 2 , et | 
Indeed, a somewhat different way of expansion into series of 
l—z 1 eral 
TER 
1 By. «laf 3.0, raf wie a? 3:0 wae Mj: 
es Er lee ET ln 
8 a’ j Az 4.5 2" 32D a” i 6 2" ‘Gi 2 ate 
=o et NIVE AS! Poa ae Fae GPL ET 
mf a paf 3 a 2 6 af 
(ate) ela rr) + 
+ i. A mars eee 
ENNE: 
~ 
+. )+ etc. 
