# Accession Number:

## AD0614810

# Title:

## INDEFINITE INTEGRATION BY RESIDUES, II,

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1965-02-01

# Pagination or Media Count:

## 19.0

# Abstract:

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.