318 PROCEEDINGS OF THE AMERICAN ACADEMY. 



and putting 



X2 _ ^2 ^ ^H\ /"^^ = Kdt, 



a/A" - K=^ 

 B = K e-^'t J(^rVl + f) J (KaVl + t^) dt, (18) 



which by means of the formula 

 becomes 



^ = k/ > >,-..elz:iH^)'^_^I"\W'll +J')^^^ 



Jr»oo 00 P = a 

 s = Op=0 



~\^P^o.-eo 2^^\j.l(s-p)lY q\{s-q)\Jo' ^* 



~" " J^ ^Q^Q 22('+'») (/ ! m ly n\{l + m - n) ! c2'*+i ' ^'^^'^ 



/=00 TO = 00 



; n ^n 2'+™ (/ ! m 1)^ ^^ 



1 = m = ^ ' n = 



/ - (/k)"+1 (- zY 



\n ! (w + 1 



)(/? + 3) . . . [w + 2(/+ 7w)+ 1] 

 (2w) 



+ 



2'+"* w ! (/ + m 



1 \ 



— n) \ c2'i+i ) 



