292 



X 



2*fW (.t-) = 2cf (x) + fif{3) [— hl, + 6/, -47, -f- /,] d^. 



o 

 Multiplying these equations respectively hy 4. 5, 1 and adding 



we get 



X 



[2y(4)(.t;)] + 5L27-(-2) {.V)] + 4[/(.r)] = 2<f{w)] +J(f{^) [A+Z;] d^ = 



where 



X 



J ^—^ 



o 



+ è (C4A + C3/, + f,/j„ + . . .) 





lil this case therefore the solution takes the form 

 2cf (..) - [2V-')t..)] - 5 [2Ji%v)] - 4 [f{x)] = 



X 







4. Proceeding now to the general case, we may expect, ^/O^) being 

 constants, 



= {-\)r.Ap\if{^) '' /\J^ . (13) 

 



If p be even the last term in the first member is — A^ji;'' [2/^^M'^")]> 

 and if p be odd it is - A'^^[f{.v)]. 

 The second member now reduces to 



X 







