DIFFERENTIAL EQUATIONS 211 



9.42 Fractional Differentiation and Integration. 



In the following expressions, i stands for a function of / which is zero up 

 to / = o, and equal to i for t>o. 



9.421 



( 2n 



9.422 



^> i = o 

 , 2 i = p n i = 



9.423 



r* = -i/- 



9.424 



p* r(i + v) 



where v may have any real value, except a negative integer. (Conjectural.) 



9.425 



-P- I= ^ 

 p - a 



-i- i - i (' - i) 

 /> - a a 



9.426 With /> = aq 2 , \ 



I 2 cr . . . (2H I) 



