287 



If 



/'>) = ,•„/,,(•'■) M-,M''') I '-J-M) \- (4) 



(licii 







The object of the present |)aper is to show tluil more general 

 integral equations may be solved in the same manner. 



2. Let 



.T 



f{.v)=Ji/{i^)I,{.v-i^)d^l (Ö) 







where p represents an integer, and let 

 then 



X 



È c„M,v) =z 1 b„ fui^) I, {.v—i3) d^ (7) 



/^+i J 







Therefore the integral equation (6) will be solved if we can 

 determine the coefficients b in function of the coefficients c. 

 We shall first show that 



.r 

 



can be expressed in a series of Bessel's functions. 

 By differentiating we get 



du r dIJx—B) 



-jl {^)-J^-^d^ 



dx J dx 



d'u r d'l.Lv - {?) 







,'M.v-ii) ^ J__ dl^^ + ! 1 - ^-! /,(—.*) = 



Now 



dx^ .i' — /? dx I i'V — Mi" 



or 



dU^,{x-ii) p^ 1 dI,X^.-ii) 



