122 



BIRKHOFF AND LANGER. 



We have, further, 

 b 



f WaYifl) (8**) Z(t) R(t) F(t)-dt = 



r n ( 



Whkip)] 



«r m ^v«- v« dmp + 



kl>mp(!)] 



d pq y g (t)Ut)dt) 



o 



A-l 



+ 



1 



X 



A 



1 



X 





_ e -^W-^»>/ A (6 - 0) + /»(« + 0) + 



6 , 



/ e " UiW |pW«" B * (<) | <ft 



+ » 



X 



the last form representing as heretofore the result of an integration 

 by parts. The multiplication of this matrix by the matrix (115) 

 yields the result 



J.- = 



- 1 



y \{r i (x)-TAb)5**\ + B i (x)-B i (b)5** /.n ul (o) A ** 



Z- e ' ' ' "u 1 ' ' **T ik {K) w kh d hh 

 fc.A-1 



6 



|/»(a + 0) - ,T M V«- J V»/ Jk <fc - 0) + / <T Xr A (0 1 {/»(i)r B » w }(ft | 



+? 



