Many-valuedness of the finite part integral

Authors

  • 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.

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Published

2018-05-29

How to Cite

[1]
RLYC Fallorina and EA Galapon, Many-valuedness of the finite part integral, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-PC-38 (2018). URL: https://proceedings.spp-online.org/article/view/SPP-2018-PC-38.

Issue

Section

Poster Session C (Mathematical Physics, Optics, and Interdisciplinary Topics)