A generating function and a convolution for the Bernoulli numbers arising from finite-part integration

Authors

  • Angelika Joie S. Tagupa ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Eric A. Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

Using finite-part integration, we uncover a generating function and a convolution of positive even Bernoulli numbers arising from the finite-part of the divergent integrals ∫0 csch t dt and ∫0 csch2t dt. This is done by utilizing the splitting property of the finite-part integral and through its Mellin transform representation. Other convolutions from applications of the results in this paper are then presented.

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Issue

Article ID

SPP-2022-1D-05

Section

Theoretical and Mathematical Physics

Published

2022-09-27

How to Cite

[1]
AJS Tagupa and EA Galapon, A generating function and a convolution for the Bernoulli numbers arising from finite-part integration, Proceedings of the Samahang Pisika ng Pilipinas 40, SPP-2022-1D-05 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-1D-05.