570 On the Partial Fraction Problem. 



\i(-^l/- i ^( a+ i:r l )( /3 r)--- 

 ■ + l(-i)^ + r ( -i)vej5^ T i )(^r i )^ + ,^ w (25) 



since the second double summation gives zero terms when 

 a = 0, and the third double summation gives zero terms when 

 0=0. 



Adding the three double summations in (25) we have 



\K+ll 



But the sum within the brackets equals 



(« + £ + *)! _ (« + £ + *) ! (£ + *)_! _ /« + £ + A /£ + t\ (97 . 



a\ J3\ tl ~u\ (0 + t)\ /3! t! \ P + t )\ t ) W) 



Therefore 

 [—] 



