Solving the Stieltjes summation problem by finite part integration

  • Christian Dacoycoy Tica National Institute of Physics, University of the Philippines Diliman
  • Eric A. Galapon National Institute of Physics, University of the Philippines Diliman

Abstract

Using finite part integration, we were able obtain a solution to the Stieltjes summation problem. The prescription consisted of reconstructing a function from a finite string of moments. This reconstruction is then used in the expansion of the Stieltjes integral by finite part integration to obtain meaningful values of otherwise divergent Stieltjes series. The prescription is then applied to the eigenvalue problem of the quartic anharmonic oscillator which showed remarkable accuracy for obtaining the ground-state energy eigenvalues from the Rayleigh-Schrodinger perturbation series.

Published
2019-05-23
How to Cite
[1]
C. Tica and E. Galapon. Solving the Stieltjes summation problem by finite part integration, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-2D-07 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-2D-07.
Section
Theoretical and Mathematical Physics