344 Rev. G. Phillips on the Summation of Series. 



Similarly, 



r — -/* -—- r — V ■=. u ,.v— 4 u „. v+ 10 . 2< -.V 



Jy.yJy.yJy.y — '^ ^-"-^ "^-^ "^ 



~ "' ■ •^- 1.2.3 Jy. yjy. yjy. yjyjy- 1 -j 



1.2.3 



and cLr^rl, 



Jy- yjy- yJy-y 



- ^^^-^}...v=.xi^_^.y-n.u^_^.y^-n:W^l^u^_^.y 



5\ 



— w. m+r.m + 2^ ... — m + « — 2 



+ u. . y 



1.2.3 ' -^ 



9K.JW + 1 ...m+n — 1 /* J_ /^ J_ ^ /* /* 1 



- 1.2.3... -?i Jy. yjy. y '" "~" Jy.Jy. l-y 



which between the limits of y = and y = 1 gives 

 (-^ + -^ + ^^ + &c. ) 



/I 1 1 o > 



+ « • M-L^( Y^;^ + 2;;i^2 + 3^^, + &c. ) 

 &c. 



^"^ + 1.2.3...« (l^+ -2^ + ^ + &c. ) 



., , 7K.7« + l\. .?« + ?«— iV 1 /* 1 ^/* /» 1 



Also + — :, — ^r—- / —/ ...n—l/ / 



- 1 . 2 . 3 ... 71 Jy. yjy . y Jy.Jy. 1 -y 



m.m-^-X ... m-\-n — i! . 1 1 ^ « \ 



~ - 1 .2.3... n \ 1 .2" "^ 273" ■*■ sTi" "^ ) 



which series is summed in second article. 



[To be continued.] 



XLVIII. On 



