Finite part integration of the Stieltjes transform for entire functions: Pole singularity

  • Daniel Anthony Monge National Institute of Physics, University of the Philippines Diliman
  • Allan Christopher Zeta National Institute of Physics, University of the Philippines Diliman
  • Christian Dacoycoy Tica National Institute of Physics, University of the Philippines Diliman
  • Eric Alvarez Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

Using finite part integration of the Stieltjes integral, we were able to obtain explicit and novel representations of Stieltjes transform of several entire functions that are otherwise non-trivial to compute and are not amenable to symbolic computation in leading computer algebra systems. The relevant finite part integrals used in the calculations are exclusively those for which the singularities are poles at the origin.

Published
2019-05-21
How to Cite
[1]
D. A. Monge, A. C. Zeta, C. Tica, and E. Galapon. Finite part integration of the Stieltjes transform for entire functions: Pole singularity, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-PB-04 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-PB-04.