A~ r (i - u)-*e~* u du 



r 



+ c 2 e-t I (i + u)-*ir*e 

 = Cl f V'(i - u)~*e-*du 



Jo 



/ 

 *-*(i + u)- 



DIFFERENTIAL EQUATIONS 



- r, i - q, Q = Cl 



- r i - 



8.555 <o, ?>o, 



g = w + 5, where is a positive integer and s a proper fraction. 



^>o: F(i - s, i - p, Q = a I u~ s (i - u)-Pe~Z u du 



Jo 



roo 



+ c 2 e-t I (i + u)-u- 



Jo 



<o: F(i - s, i - p, Q = ci /u- 8 (i - )-*-* du 



Jo 



+ c 2 I u~ 8 (i + u)-* 



Jo 



8.556 pure imaginary: 



P = r -> % = s t where r and s are positive proper fractions. 



i: 



, s, Q = ^ j$f- l (i - u)'- l e-* u du 



+ c& 1 -*-* j u~ 8 (i - u^e- 



> s , Q = ^ I *u r - l (i - u) s ~ l e~t u du 



Jo 



+ c 2 ju r - l (i - u)'- 1 e-* u log I %u(i -u)\ 



du. 



8.600 The differential equation: 



d z v N dv 



x w +( t-^T x - ay = 



is satisfied by the confluent hypergeometric function. The complete solution is 

 a, 7, x) + crf"^ M(a -7 + 1,2- 7, x) = Jf(a, : 7, *)^ 



