THEORY OF CONVERGENT SERIES 103 



Substituting the value of E from equation (16), we have 

 -FZ+- 5 -F 2 Z 2 - Y*Z*+-2ti-Y*Z*-e 



2 24 72O 8064 



2-3 2-3.4.5 2-3.4.5.6-7 



Multiplying the two series together by the ordinary 

 algebraical method, we obtain 



=E 8 Y(i - - FZ+ F 2 Z 2 - -^F 3 Z 3 + F 4 Z 4 - etc. 

 V 3 i5 3i5 2835 



as given in Table VI of convergent series. 



