DUNKEL. — LINEAR DIFFERENTIAL EQUATIONS. 351 



I. Rr^y Rr,. 



(27) ^,,,,^, = x^^-'<% f'Ux... 



C 



c c '=1 J=l 



t integrations 



where h,j is a positive integer whose value it will not be necessary to 

 write out, noting, however, that : 



(28) h,,<e,-X. 



II. Rr^ = Rr,. 



a) k :^ K. I < L . 



X 



(29) c/...,,^, - :r^^-'-'' V {''- dx . . . 



i—m j—Ci 



(30) 



X 



Jl./xJ^-'^.-^> 2 2 ^i:ii-. <>u. (log xf'Jdx. 



*— ^ ^—^ 



grations 



*"'*■ = (1^1./ V^ •• -/i "^^J;^"'''"''"' *"- "- 







< integrations 



c c c 



(^ — Z) integrations 

 / 7 r ^ XX ■ . 



+ 2 fl''--:fl''-f--'''-^'' 2 2V:i.-,*.;,aog:.)'-v&l. 



— /• ^ - i=l )'— 1 -J 



c c c »=1 ^=1 



t integrations 



C) k = K, I < \. 



f=l ^ 



(31) </>.,,,^i=2 f-,^^-.. 



'-^ 



* ] iS *="* •^-*« 



• • • f ^^-^ r 2 2' i«,V.«^,.y..(logx)*'./tfe. 

 'o ^=1 J=^ 



t Integrations 



