I2O MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



6.364 



log (i -f 



= 03 + 0102 + 7 01) 

 



I 2 , I o , I 



= #4 -h 0103 + ~ 02 + ~ 0201 + "~ 

 22 24 



6.365 



I 



2 



I 2 



123 



C4 = 04 - Cl03 -- ^202 - 



444 



z = 



6.37. The Multinomial Theorem. 



The general term in the expansion of 

 (i) (0 + dix + 2 2 + 3 # 3 + . . . . ) n 



where n is positive or negative, integral or fractional, is, 



Cl 1C2 '^3! . . . 



where 



Ci, ^2, ^3, . . . . are positive integers. 



If n is a positive integer, and hence p also, the general term in the expansion 

 may be written, 



