148 Mr MURPHY'S SECOND MEMOIR, &c. 



Cor. Put .; — r = ^» and the series 

 \—n 



t~^ = (\~.h){ T„ +T,h+ TJi^ + &c. \ becomes 



^^=^+ ^■•r4T^+ ^-7;:ttv3 + *'^- 



The principles which have been used in this Section to obtain ex- 

 pansions such as the preceding by means of reciprocal functions relative 

 to simple integration, will apply with equal simplicity to reciprocal 

 functions relative to any number of integrations. 



R. MURPHY. 



Caius College, 

 Bee. 18, 1833. 



