Many-valuedness of the finite part integral

  • Rossjyn Lian Yao Corres Fallorina National Institute of Physics, University of the Philippines Diliman
  • Eric Alvarez Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

We considered the finite parts of divergent integrals of the form ∫ab g(x) (x-x0)-n dx for a<x0<b. It is shown that the finite part takes on a broad range of values, depending on how the contribution of the offending singularity was removed. A conditionally convergent logarithmic term appeared for cases in which the two radii of the contours used possessed a linear dependence towards each other, proving that the finite part could take on many values. The multi-valued finite parts were finally expressed as contour integral representations in the complex plane.

Published
2018-05-29
How to Cite
[1]
R. L. Y. Fallorina and E. Galapon. Many-valuedness of the finite part integral, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-PC-38 (2018). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2018-PC-38.
Section
Poster Session C (Mathematical Physics, Optics, and Interdisciplinary Topics)