204 PROFESSOR A. E. H. LOVE ON THE 



On substituting for the three series in the expression for A 2 we find 



A - Aa '[J_ -H-- -- 

 1 



L7 45 / 45 



. ^ _ 

 rcr s 4 a 4 \ na* 



30. Again we have, when h* = and P = 0, 



( 



J 



5a aa 

 and with the values already used for f a , . . . this gives 



Ari-^4 



fe 1 

 5)"j 



- 

 5vL6 2.7 2.4.7.9 2. 4 . 6 . 7 . 9...(2ic+5) 



8AT1 8s 3 a S.lOsV , y(2K+2)(2/c + 4)(2ic+6)^a 2 ' 1 



^~L7 2.7.9 2.4.7.9. 11 ~ 2. 4. 6. 7. 9...(2 + 7) "J 





~ 5v\_ 6.7 2.7.9 2.4.7.9.11 2 . 4. 6 . 7 . 9...(2*+7) 



The first of these series has already been transformed into 



IG^LV s 2 ** 3 s 4 a*J Jo \s a a a s*ct*/j 



By means of the identity 

 (2/c+2)(2*+4)(2>f+6) = i L_ 9 15 



(2/c+3)(2ff+5)(2ff+7)" 2/c + 3 (2*c+3)(2c+5) (2K+3) (2 

 we transform the series 



into 



Ifi %y? (-Y _(2^2)_(2K4)^_ 



s|_7 2.7.9 ' 2.4.6.7.9...(2ic+7)"j 



l\' / 3?x*-\/'Lx > x 4 /I x* a; 4 



16Li 1 ~^ + ^~''V 3 \3"O + 3T5^~"7 +9 l3T5~3^7 + 3.5.7.9~"7 



., 



V3.5.7 3.5.7.9 3. 5. 7. 9. 11 

 which is the same as 



