INHNITK SKlIIKs OF ANALYTIC FrXCTI<)\- 

 Then 



taken along a suitable path, satisfies tin- o|ii;iti<n (IX), and thru- an- in -.-n.-ral n-1 

 such integrals, linearly independent. 

 For 



on integrating by parts, where it> {m} (t) dcimti-s (i*if>(l)/(lf. 

 Let 



Sulwtitute in the left side of (18), and subtract the /.-r i|uantity 



and the expression l>ecoines the integral of a |>erfect difTerential. 

 Hence 



satisfies the e(|iiation (18), provided that 



has the same value at the beginning and the end of the path. 

 Let the roots of the equation 



^i" = 0, 

 supposed all different, be denoted by 



A|, Ay, ...X.. 



The points 



; = X,, s=X, ...c = A,, and : = 



VOL, cciv, A. :i R 



(19) 



