certain Bessel Integrals. 335 
where X< I, and F is the hypergeoinetric series given by 
F (a, 6, ,, «) = 1 + T c + gT^^iy- 2 *" 
a(a + l)(tt + 2)^ + l)(/, + 2) 
8!c( c + l)(c + 2j *-+•••• 
Then, using the same method, we obtain series for more 
general integrals suitable for large values of p. We obtain 
thus 
r-* TMT .v, ", ^ (2s4-2)lF(-5-l, -j, 2, \ 2 ) 1 
J «=0 5.(5 + 1)12 ^> 
(10) 
/* s =o s!(s + l)!2 p 
« J iWJi(V)-f = X2(-1) , f/ . 1V9 2,+2 2^+r 
-A^ 1+6V2+6X4+X6) ? + ]• • ( 12 ) 
To obtain series suitable for small values of p we have 
= 1 COSarfa | ^"~^J (2/ ( 6COsia)rf/x- 
7T 
_2 T ¥ cos 26 d6 
~ 7? 1 V^ + ^COS 2 ^' 
The summation in this integral is now divided into two 
parts, one between the limits and — — e and the other 
between ^ — e and e; e may be taken indefinitely small 
2 A2 
