Chessin — On Some Relations Between Bessel Functions. 101 



)i being an integral number, then the function v will satisfy 



4,n^ — 1 

 the equation (3) when/ (a?) =a2 — — j—^ — , while the function 



10 will be a solution of the differential equation (3)' when 

 <f>(x) = ^_i^^^. Therefore, by (4), 



Likewise, n still being an integral number and the func- 

 tions /(x) and <^(x) being selected as above, if we take, in 

 succession, 



(5), V = l/^J'„(ax), w = VxK^{l3x) ; 



(5)3 v=.VxK^{ax), to=VxK^{^x)i 



we obtain the formulas 



= (a'' — ^^)xIi„{ax)KJJx). 

 When n is not an integral number we take successively 

 (7)i V = VxJ^^(ax), w = VxJn{/3x) ; 



(7), v = VxJ„{ax), iv = VxJ_,,{^x); 



(7)3 V = V'xj_,^(ax), 10 = VxJ_^(^x); 



and arrive at the identities 



= {a'^—^-^)xJ,,{ax)J,{^x), 



