( 740 ) 
replaced by a; as may be seen by putting y= a and integrating 
between « and A, 
Thus 
Un Apt) — dn—| G49 +...+(—1) Aytnti = 0p = OA ea 
and this relation proves that a, + a, 2 + a, à° +... is a reciprocal 
series, Which may be written 
—l Pee 1 ae 
ha de aie UC ke 
where 
bi lj Oper Op 1.0, te jee dj see Dela rp = 0.1.2.2 
or, according to (11) 
Hence, if 7 be infinite 
rn AN a, — 2u, d 4 34,7 — DCA 
a, a She ti, Ae > er See SS SS 
1 — ud Hadad — D (a) 
or 
8 U da sie 
— 4,2 — — #— — 7? — 
: 2 2 
1) 19) =e 
Writing this equation 
ad ee a, 2? 28 As an =e An—l an—] Me An dire Onl onl rv 
: 2 2 n—-1 n n+l 
Daye Ey = 
Zr : nl 
=] + (—1)" (A,° — — Al ——— + .-.. 
"nl we (n+-1)! 
it is evident that the first member is independent of a,a,..d,—1- 
If therefore 
D(a =1— Ars hye ek, 
we have 
2 a3 an et 
(: —Ai+A, Tas Aste led: Bie ER Ra 
dd 
or finaliy 
AO (14) 
and 
AA =i), 
In the same way it follows from 
D (aya) = D (a) {K, 4+- AK, 4+ 2 Ky 4+ --} 
