20 
will be 
r i 
2 
5 
" 3 
6 
9 
12 ’ 
12* 
12 s 
;rF 
IT 
12’ 
12 3 
; x 3 
; x 
1 
2 
1 
2 
1, 
4 
l 3 * 
IT* 
. 3 ’ 
“8" J 
^F 
_7_ 10 13 
12 * 12 ’ 12 “ 3 
; x 6 
There is a little (incidentally) on these ultra-hypergeometric 
series in Krunmer’s valuable Memoir on the hypergeometric 
series, Crelle, t. xv. I attach no value whatever to the trans- 
formation of the series into definite integrals. As to your 
own remark ‘ what is wanted is the solution without the aid 
of definite integrals’ — it seems to me that the series is the 
solution, and that what is wanted is a study of these series, 
so as that they may be considered as known transcendents ; 
which, considering the great extent of the theory of the 
simplest case, that of the hypergeometric series, is likely to 
remain a desideratum.” 
