( 499 ) 
If we now put in the first integral 8 = a@ — y and in the se- 
cond one B=a + y this becomes 
x 
a ik JAG) a L (ay) 
Se ie OY + fz, Bj |} 
4 Omi a+y el 
0 0 
with which equation (1) assumes the final form 
wc 
2 : Ge L (ay) . I, (a+y) 
= n I, (a) I, (x) = A fr (& — 7) | : Ii — t dy. .. (4) 
. oH 
d a—y a+y 
A closer investigation of formula (3) teaches us, that it holds 
good for even values of too, also that many analogous relations 
exist. So we find inter alia, # being any integer, 
eile —p Ly 
{2108s 
a—p n 
0 
* Lijn 3 Ihe C 
fn («—8) apa 
0 
a 
fA (e—8) Te (3) ‘ 3 = Zaft (a) 
a—p n 
0 
el aml 3 1 Te Js 5 
iS ze TN (8) dp: =S (a) 2 (a) . 
(a—Bp)’ 2n li n— 1 ntl 
v0 
4 
| I, (a— 8) I, (8) d8 = sin a. 
0 
We shall not dwell upon this at present; we only remark, that 
when a very great positive value is assigned in (1) to 2, so that 
ee 2n+1 
NDSS ye COS (« == Sar ), 
HU 4 
I, («—a)+ 7, (#—a)=2 yok cos (« — =) cos Ct, 
Ey di 4 
2 mr 
I, (@ —a-+ Bs) —TJ, (e + ae — ~)=2 sin (« — =) sin (a — B). 
nt 
This changes (1) into 
we find 
24 
ra nr a OD (len (B) 
Sn Re ds pe TENG ; 
= n Ly, (a) sin Dg sat =a | ar sim (a — B) dp 
es < a =. t 
0 
