INDEFINITE INTEGRATION BY RESIDUES, II,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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If Fz is holomorphic in the extended complex plane except for a finite number of singularities, and if Fz is holomorphic on the open arc cos a i sin a ... cos b i sin b of the unit circle except for simple poles, and if Fz is holomorphic at cos a i sin a and at cos b i sin b, and if a b a 2 pi and u b-a2, then the Cauchy principal value integral with respect to v of Fexp iv from a to b is shown to equal i R s. R the sum of the residues of Fzz log exp iu z-exp iaz-exp ib for z in the extended plane but not on the closed arc from expia to expib. S the sum of the residues of Fzz log exp iu z-exp ia exp ib-z for z on exp ia ... exp ib.