of Definite Integrals. 13 



Tlien also 



and 



or 



Operate with ( y j on both members, and we have 

 by making a— ;r = «t;. Therefore 



A 



Next, let (p (a?) = 2-^, a descending series. Then 



<p(a + a;) = 2 ^"^ 



(1-) 



and r"^ n-M ^f , N VA r"^ x^-'dx 



- ^ -^;^J^ (TT^ ~ ^''''^;^^^ r(m) -'^^''^ 



suppose. Therefore 



^, >^ A;;, Tlm—n) ,, , 



and 

 or 



