208 PROFESSOR A. E. H. LOVE ON THE 



We use the identity 



(2K+5)(2*+7) 2c+5 2K+7 

 to transform Q' 3 and then we use the results 





7 2.9 2 4 



V _ , v_ T [ 



4.11 Jo 



We thus find 

 A., = - 



+ ve -*"+?j. v (sa)- 1 fafe-dsK\. . (95) 

 Again we have, when h 3 = and k 2 = 0, 



and here we have 





a ^Qj_ / . _3AT J_ *c? 



o< 7^ L 7.9 2.9.11 2.4.11.13 " 2.4...2ie(2jc+7)(2ie + 9)"j' 



while the other series can be obtained from those written above. We use the 

 identity 



2/c-l 4 5 



2<c+9 



to transform the series last written, and we use also the results which we used in 

 obtaining the expression (95) for A 3 , and find 



63 = ~ [l2(sa)- 7 ^x*e-VJx-15(sa)- 9 ^x 8 e-^dx+Wv(sa)-^ M x 8 e-Vdxl . . (96) 

 We find also the results 





