Lei /11 and /1 be integers. \vhere 0 .:::_ /11 < 11.
Chapter 0, Problem 7.11(choose chapter or problem)
Lei /11 and /1 be integers. \vhere 0 .:::_ /11 < 11. follmv the s!eps belmv to derive the inlegration formula l '.\,; .r 21 " ;r ( 2111 + I ) , clx = - csc ;r . . 0 .r- 11 + I 211 211 (ll) Show tha! !he zeros of !he polynomial : 211 + I lying above lhe real axis arc [ . (2k + l);r] q =exp / 211 and that there arc none on !hat axis. (/.: = 0. I. 2 ..... II - I) (/>) With the aid of Theorem 2 in Sec. 83. show that -~" I )it2.( I 1u Res -,-~-- = - -t .~ =< ~ : :JI + I 211 (/.: = 0. I. 2 ..... II - I )where c.l arc the zeros found in part (ti) and2111 + Ia= ;r. 211Then use the summation formula(:: f. I)(see Exercise 9, Sec. 9) to obtain the expression11-I _:!111L ' ;r 2;ri Res , = .:=<1. -- 11 ~ I II S0lll"' .
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