348 ON THE DEFINITE INTEGRAL OF THE PRODUCT 



The coefficient of /i*-- 1 in (^-l) 2p is 



and therefore the absolute term in - ; ..^p- 1)^ is 



dp. 



(2p)\(2p-r-l)l . }f 

 r+W, L. , '+ 1 \, V 



2 

 Again the coefficient of ^' +r ~ l in (/r- 1 )'-''' ' is 



r+l 



2 . 



(* 



( ^ + /-l 



and therefore the absolute term in , .,, l+r _ l (^ I) 2 ' 7 " 1 is 



2 ; : v^^ 



therefore the value of the above general term when fj. = is 



(2p) ! (2j>-r 1)1 (2</ l) ! ('2g + r 1 



_ -, y +5+ r 



r+l\, 



t- 



r - f~ TO ?t m.-r-l n 



he> ^ ' /-HI - r - 1\ , (m + r + 1\ In - r\ J 



\-2~- ) l ( ~ 2 ~ ) l \ 2 j : i^"- 



Dividing by 2 m+n m ! n ! and changing the sign, we have 



m+n+l 



-(-^~ ~ (m-r-l)! 



,'n-r 



/ m -r-^\ ? /ffl + r+l\ , ,'n 



\ 2 ; v 2 / v 



2 2 



where r is to be taken equal to the odd numbers from 1 to n. 

 This general term may be put under the form 



3 ' 5 ra-r-2l .3.5 ... 



.4. 6 ... (n-r) 



