1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

12.7 • SHIFTING THEOREMS AND THE STEP FUNCTION 555

y y

y = u. (t)ftt-a)

0 a

Figure 12.23 Comparison of the functions f (t) and Ua (t) f (t -a).

• EXAMPLE 12.17 Show that t:, (tne"t) = n'..

(s-at+ 1

Solution If we let f (t) = tn, then F (s) = £, (tn) =

8

:~ 1 , and if we apply

Theorem 12.15, we obtain the desired result: