18 THE REV. F. H. JACKSON ON 
The general term in the series Q’, (#.) is 
[n+ 27 r|! [v+r]! (2 ae fe, ala oy Ig l—n—2r— 1) 
(r} n+ 2re 112 
so that 
@” Qin(Xr) 22 [% ate 2r|! [7 ay r|! (2), wr { Se 1] : [ = v] rT) —r—2r—-1,,p"[—n—-27—-v—-1] 
Pape pln tener di nasal AA pacman en 
Now the general term of the series (80).may be written 
jpAt UE (ntyt 27] [utr] asrgmmon-w (3a) 
[mtv]! [7]! [22+ 27+ 1]! Sy 
so that if we give to the arbitrary constant A the value 
7 v-1 [n+ v]! 
[2n +1]! 
and denote the series by Q,,,(«A) 
then 
Qim(@A) = > paras T) ai or : ae 
and 
dO wvtl oy y 
Ge EP). 
ey Ll ay . | 
pa FP Ep? da + ete. 
1) Teese), 
7 py Yy any 
De de® 2 de® * oa 
equation (34) would have taken the form 
Ab” Qin tA) 
dg” 
VIVAL yg % 
= ’p 2 Qing x” Xd) 
Qin(,A) satisfies 
ae” Qin 1 q®) fa fl nv 
ia Pra - a + eee [- noy-1] ba oy [w-v][- n—v—1]Qin 
= 2p | Qin@ dv") - ae 08 ea || ee 
To find the sum of the coefficients of « in the series Q,,,; we make the following 
substitutions, 
m= — n+l 
=2 
y=nt+vt+2 
Zz=—l 
c= —N+V 
in the series (11). 
