v 
Gever 
f (cos x—cos py! 
2¥-1 ya 1 (v—1) eos°y—! 5 z 
x 
(1) 0 : =) 
v 2 
C (cos x) = feos ¢—cos x)?- 1 
x 
4 v/a Il (v—2) sin > 
2y—1 Ag . 
ee (sin a) sin p dp 
2y-—3 
Aces 
y 2 
Cc (cos v) = {eo A— COS g)’—1 
n x 
lynn LT (v—2) cos°v-! = x 
2Qy—1 p 
C (cos = sin p dp 
2n+1 
which are a generalization of the integrals: 
x 
2 AR 
Pr (cos A= =f ae (x ar 2) 4 Lp 
a V 2 (cos p — cos 2) 
0 
8 Dad 
Py, (cos) = sin (n + 3) 4 dp 
tJ) V2 (cos x — cos g) | 
x 
AE 
v> 4), 
v>), 
given by MEHLER in his communication “Notice on integralforms 
of Dirichlet for the spherical functions P, (cos 9) and an analogous 
integralform for the cylindrical functions Z(z)’, “(Notiz über die 
Dirichlet’schen Integralausdriicke für die Kugelfunctionen P, (cos #) 
und eine analoge Integralform für die Cylinderfunctionen Z(e))”’. 
By putting 2 equal to the root of the function C (cos 2) lying be- 
tween 0 and > we transform them into the following relations: 
