ilNillT llllA>l<y .IM' ul'IK.I I IdX.II. C.ll.i CIA'S 727 



'I'o priivi- this ilu-orrm wr si.irl with iho intfKr;il ('({ualions 

 1 



PII(P) 

 1 



= / h{t)e-'"dt 



=£'''' 



e f'dt. 



prnp+y.) 



Ill ihi- tirst nf i1r's<' ctiii.itions rri)lacf tlic symbol p hy q-\-\: we get 



-L • n, Xr>= r Ht)e->^'e-'>'dt 

 q + \ //((/ + X) Jo 



and ihfii to preserve our original notation rei)Iace the syniliol (/ hy p. 

 whence 



The inlei;ral etiuation in g(/) can be written as 



{'+j) iP+miP+xr fo '^'^'-"'' (^^ 



Comparing equations (a) and (b) ii follows at once from theorems 

 I and II that 



g(l)=(^l + \f'dtyi(t)e-^'. 



From the foregoing, the following auxiliary theorem is immedi- 

 ately deducible. 



Theorem 1 'a 



If h=h{i) and g=git) are defined by the operational equations 



^ (p+\)ii(p+\) 



then 



g{t)=h(t}e-K 



The proof of this theorem will be left as an exercise to the reader. 



