200 Dr. L. K. (Jr. Filon on a iVeiv Mode of 



multiple of the coefficient of 11"^-""-^ in the expansion of 



f= ^_ ^, . . . (22) 



i/r being expanded in a Laurent series in u and in inverse 

 powers of t. 



10. We may now show by direct substitution that i|r 

 satisfies the differential equation 



For 



^ ^^-^^d^ ^.77' dt - i^L (^7f ) =^- (2^> 



— ^ =1- J^ / _ 1 \ 



whence 



|{"-'*''f7*}-i^M'-''-vf^'("-:))i 



=^^-{'-S7fc.("-',)l{'-'"-1^"l=-4"-D} 



VI -A'' 



...{-..-(^p!-^-^)(,.-!)( 



'T(("a)=-2'+'+2'"+'- 



I w^hich 



From w^hich 



A f 



= after some easv reductions. 



