Reversion of Power Series. 373 



'(b) Solution of cubic. 



(1) y=za % + a 2 a? 

 ~z=x—b 2 x z 



^;+M + 3^ 5 +126^ + 55^ 9 + 273^ 11 + 1428^ 3 + ... . 



(9) y = a <v + a 1 .c 2 + a 2 .v :i 



^=. H -6 1 ^ + [ &2 + 2& 1 2 ]^+[56 1 ft 2 +5& 1 3 y 



+ [?>b 2 2 + 21^% + Ubf]z* 



+ [28M 2 2 +84&i 3 6 2 +426 l 5 ]2« 



+ [12 V + 1S0W + 3305A + 132^ G ]r 7 



+ [165M 2 3 + 000?^ 2 2 + 1287^ 2 + 4295 1 7 ]^ 



+ 



(c) Solution of biquadratic. 



(1) ( y = a 0t r + a 3 .r 4 . 



JB =z + b z **+±h*z'+22hh"+U0h*z™+ - • 



(2) ^=a a?+fl 2 « 3 + fl 3^ 4 - 



«8 



= .<■ — Ao,/ ,:] — ta.* 



> 2 .C ^3<c' 4 , 

 ,6 



# = ~ + 6.,c 3 + b z z* + 36 2 V + 7& 2 M ( 



+ [46 3 2 4 12/> 2 3 ] c 7 + 45 7 ^ 3 : s + [55W + 555 2 4 ]* 9 

 + [22V+286i 2 3 ^]^ 10 + [546W+2736 2 5 ]s u 

 4- [455 W+ 1820 V*»] - 12 + [ 14 °V + 4760 W+ 1 4286 2 6 >» + 



(3) ?/ = O # + a v r + fl'o.t- 3 + a 3 ./ ' . 

 2 = # — b v r 2 — b. 2 .r :] — b z X l . 

 ... = ^ + ^+[& 2 + 2i 1 2 ]: 3 +[/>3 + 5M-2 + 56 l 3 ]> 1 . 

 + [6&A+3* 3 2 + 21*i 3 ^ + 14ii 4 ]^ 

 + [7W 3 + 28(6 1 ^ 3 + M2 2 ) + 8^ 1 ^ 2 + 426 1 5 ]c G 



+ [8M 4 + 46 ;; 2 + 72JM + 12& 9 3 + 120AA 



+ 180W + 330^2 + 132V]; 7 

 4- [456A 2 + 45V*a + 165&A 3 + 495V5A 



" + 4956^3 + 990W 2 + 1287& 1 5 6 2 +429* 1 7 ]s 8 



+ 



