Partial Fraction Problem. 569 



Next let /3 + 7 = a / , then 



-l- i '-'i<-»>'-''--"# , -f- + r I )e"i:i"'')- 



Bat 



s( a '~f + i i " 1 )=coefficientof^" 1 inS(l + ^' 1 '^^- 1 



|S=0\ t_ - 1 / 13-0 



-("?■)■ 



therefore 



Letting /j, = K — 2a , — l3 , i then 



Q (+I , .= s (-iy ~z (- a y (*' + <) («' +|'+ ') »..«_;, 



Interchanging a' and /3' and dropping the prime signs, 

 we have 



Q (+1 ,«=2 ] T(-^(-a)^ + < + 1 - 1 V a + ^ + ' + 1 - 1 ) mi c- 2 a-.. 



/S = 0a=0 \ P /\ a / 



which is of the same form as the expression for Q^ K » 

 We finally show that (22) hoids for Q*+i K +i. 

 Now 



Qt+iK+i^QtK+i — aQt+i* — bQt + i K -i 



- i [ |!-n. 1 .(' 3 r)"l*(-i)-»-c^r) .—. <*» 



