Author Archives: Eric A. Galapon

E.A. Galapon, “Regularized limit, analytic continuation and finite-part integration,” https://arxiv.org/abs/2108.02013

By | March 4, 2022
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Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567 (2017)]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the… Read More »

L. Villanueva and E.A. Galapon, “Finite-part integration in the presence of competing singularities: Transformation equations for the hypergeometric functions arising from finite-part integration”

By | December 5, 2020
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Finite-part integration is a recently introduced method of evaluating convergent integrals by means of the finite part of divergent integrals [E.A. Galapon, {\it Proc. R. Soc. A 473, 20160567} (2017)]. Current application of the method involves exact and asymptotic evaluation of the generalized Stieltjes transform $\int_0^a f(x)/(\omega + x)^{\rho} \, \mathrm{d}x$ under the assumption that… Read More »

D.A.L. Pablico and E.A. Galapon, “Quantum traversal time across a potential well,” arXiv: 1908.03400

By | August 12, 2019
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Abstract We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA)-operators. This is done by constructing the corresponding TOA-operator across a potential well via quantization. The expectation value of the potential well TOA-operator is compared to the free particle case for… Read More »

C.D. Tica and E.A. Galapon, “Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. II. Non-integer orders”, Journal of Mathematical Physics 60, 013502 (2019).

By | January 3, 2019
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Get your copy here from the publisher. Compare with the original version of the paper, especially Section 3. Tica-Galapon Journal of Mathematical Physics 60, 013502 (2019) (accepted version)

C.D. Tica and E.A. Galapon, “Finite-Part Integration of the Generalized Stieltjes Transform and its dominant asymptotic behavior for small values of the parameter” arXiv:1703.07979.

By | March 24, 2017
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The paper addresses the exact evaluation of the generalized Stieltjes transform $S_{\lambda}[f]=\int_0^{\infty} f(x) (\omega+x)^{-\lambda}\mathrm{d}x$ about $\omega =0$ from which the asymptotic behavior of $S_{\lambda}[f]$ for small parameters $\omega$ is directly extracted. An attempt to evaluate the integral by expanding the integrand $(\omega+x)^{-\lambda}$ about $\omega=0$ and then naively integrating the resulting infinite series term by term… Read More »