1 



228 Miss Wrinch, On the exponentiation of luell-oj'dei^ed series 



[*-33] h . Hp . D . PQ'X € 1 -^ Cls 



|-.(l).(2).*-213.Dh.Prop 



r341. h : /x €(Tp*Ayx . Hp *-208 . p'(Tp*Ayx . 



Dem. 

 [*-201] !-:Hp.D.'B^Cnv'^(Tp,\) = A: 



D h : Hp . D . E ! ?p V (1) 



|-.(l).r84.DK.Prop 



*-35. f- :. i^ [^ a^PQ'X = PQ'X . Hp *-203 . p'(Tp^AYX = A . 



ReC'P'^::)f>:SeX.Ds-RP'^S 

 Dem. 



[**-84-31] h . Hp . <Sf e X . /<: = p^K^P*-^ y^ '^'^\ ■ 



D^.Er'Q'Q^'x=5:r^Qm'x (1) 



[**-34-02] h . Hp . ^ e \ . k=p'\{Tp^Ayx nV'S] . 



D^ . gT . T e fp'k . K^e^'X = T'Q^'X . 



(2''Q„^X)P(,Sf,Q,^X) (2) 



h . (1) . (2) . D I- :. Hp .DpiSeX. D,, ■ PP^>S^ 



*-4. h : : Hp *-203 . p'(Tp^A yx = A.ze a'PQ'X :.D:.S ['Q'z 



= (PQ'X) [~Q'z : (PQ'X'z) P {S'z) .D.'3^U.UeX. UP'^S 

 Dem. 



[r04] h-.ze a'PQ'X .:>.'^pi.fMe {Tp^AyX . 2 e'q'Q^'iM : 



[r341] D h : . Hp . D : ayu . ^ = Tp V ■ 3 ■ (PQ'^) [~Q'Qm'i^ 



[r341] D h : Hp . D . a/., f^ . C/^ 6 ?p ^ ■ (i'Q*^) T Q'Qm'Tp^M' 



= U['Q'Q^'Tp'v.zQ^iQ^'v): 



[*176-19] D I- : Hp . D : ,S7 Q'^ = PQ'X [Q'z . 



(PQ'X'z) P (S'z) . D . a ^ . [/ e X . UP'iS 



