318 MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 



Again, 



n dx\_ dxj Y dx\__ dxj 

 dx\ L dx ^ dx J) 



/<j>G n x k dx= - — I x^SG n dx, from (4) 

 9n Jo 



or 



I — Qn —ix = a ffn <S 



a^G„8<£<i£ 



#11 



Similarly, 



/ 0.G n .a da: = / S<f>.G n x^dx 



Jo 3n 9 n J 



l) n v L - J x = a <S0 ) 



f a S<f>.G n .x'dx = ± { a^G^fy] -fh.(} n .x"dx } , 



and so on. 

 Hence 



= « A {G n cr^ l + <5)- 1 0} ;r=(i .... (22) 



