Follow the steps below to find f(T) when I F(s) = ~ - -.-

Chapter 0, Problem 7.54

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Follow the steps below to find f(T) when I F(s) = ~ - -.- s~ s stnh s Stan with the observation that the isolated singularities of F(J) arc Jo= 0. s11 = 11;ri. s11 = -11;ri (II = I. 2 ... . ). (a) use the Laurent series found in Exercise 5. Sec. 73. to show that the function e'1 F(.'l) ha-; a removable singularity at.\ = J 0 \Vith residue 0. (/>) L'.sc Theorem 2 in Sec. 83 to show that [ ,, _ . (-1 ) 11 i expfi11;rl) Res e f (s) = ------- ' =.>" ' II ;r and I)//. . ) I [ ,,_, -(- 1exp(-111;r1 {es e f (s). = . .1=:C ' 11;r (c) Show how it follows from pans (a) and(/>). together with series (7 ). Sec. 95. that ~ { . . . . } 2 " ( - I 11 ~ I fU) = L ~es[e' 1 F(s), + Re~[e' 1 F