Bessel- Clifford Function, and its applications. 519 



14. The definite integrals of the Bessel Function can be 

 written, in our notation of the Clifford Function, 



\ C_iui' cos 2 (j)) d<j> — I cos (2^/x cos (j)} d<j> 



. '0 2 Jo 



_ -, (-4*)* 1.3.5.. .(2&-1) 

 . ~ Z UU 2.1.6...2& 



= *" 2, (n 7;p = wC^), ....... (1; 



( ch(2v/.-c cos 0)^0 = ( (?**«»* d<t> = 7rC(-#) ? ' . (2) 



Jo Jo 



Pc^cos 2 ^)^ =7rC 1 (^), ....... (3) 



and so on. Also 



j C(* sm 2 <f>) sin 0<ty = 2 ("n^ ( ^ Shl $Y k+ld( t> 



= 9 ^(-# 2.4.6..,2^ 

 " * (Ilk) 2 3~.5.7...(2£+l) 



I, 



_ 9 ( — l.t') 7 ' __ sin 2 V ' x _ p / 



and others derived by differentiation, sucli as 

 I Ci(# sin 2 <£) sin 3 (j>d(f> = C,(#), . . . , . 



JO 2 



1 Ci(o?sin 2 </>) sin</>^> 



Jo 



-'••^ nMK^i) J^^ +1 ^ 



(5) 



....+2- '-*)* .1 



.1.6 2k 



I1AII(A + 1)'3.5.7....2A+1 



4(-4a)* 



n(2^ + 2)-*' 

 1 v (-hrV+ l L-cos2 v /, 

 4.*: ^ri(2A: + 2; 



2 2 



_ 1 (-~4aQ*+ 1 __ l-cos2 v Ae 



~ 4.^11(2/v + 2) .t- ' ' * * W 



