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Adaptive Integration and Improper Integrals [PDF]

Mathematics of Computation, 1975
Let R be the class of all functions that are properly Riemann-integrable on [0, 1], and let IR be the class of all functions that are properly Riemann-integrable on [a, 1] for all a > 0 a > 0 and for which \[ lim a →
openaire   +1 more source

Asymptotic boundary conditions and square integrability in the partition function of AdS gravity

Journal of High Energy Physics, 2020
There has been renewed interest in the path-integral computation of the partition function of AdS3 gravity, both in the metric and Chern-Simons formulations.
Joel Acosta, Alan Garbarz, Andrés Goya, Mauricio Leston   +3 more
doaj   +1 more source

Henstock-Kurzweil integral on ${\rm BV}$ sets [PDF]

Mathematica Bohemica, 2016
The generalized Riemann integral of Pfeffer (1991) is defined on all bounded ${\rm BV$ subsets of $\mathbb R^n$, but it is additive only with respect to pairs of disjoint sets whose closures intersect in a set of $\sigma$-finite Hausdorff measure of ...
Jan Malý, Washek F. Pfeffer
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Micro-Scale Experimental Approach for the Seismic Performance Evaluation of RC Frames with Improper Lap Splices

Infrastructures, 2023
Reinforced concrete (RC) frames are an integral part of modern construction as they resist both gravity and lateral loads in beams and columns. However, the construction methodologies of RC frames are vulnerable to non-engineering defects, particularly ...
Ali Javed, Chaitanya Krishna, Khawaja Ali, Muhammad Faheem Ud Din Afzal, Armin Mehrabi, Kimiro Meguro   +5 more
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Improper integral. II

Formalized Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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General Master Theorems of Integrals with Applications

Mathematics, 2022
Many formulas of improper integrals are shown every day and need to be solved in different areas of science and engineering. Some of them can be solved, and others require approximate solutions or computer software.
Mohammad Abu-Ghuwaleh, Rania Saadeh, Ahmad Qazza   +2 more
doaj   +1 more source

A New Expression for the Coulomb Potential Corresponding to the Product of Two Exponential Functions Based on the Properties of the Integral Representations of the Bessel Functions

Trends in Computational and Applied Mathematics, 2023
The calculation of the Coulomb Potential corresponding to the product of two Exponential Type Functions, inherently has numerical challenges that must be resolved.
C. J. Alturria Lanzardo, J. E. Pérez, M. L. Tardivo, G. Fraschetti, J. C. Cesco   +4 more
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Alternative Proof of Frullani's Theorem and Applications in Evaluating Frullani Integrals

PUP Journal of Science and Technology
This article provides an alternative proof for the Frullani integral formula using an approach different from the existing one. This alternative proof gave us a novel method for evaluating certain improper integrals of Frullani type.
Paul Vincent Botin, Michael Sta. Brigida, Edwin Balila   +2 more
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Multiple positive solutions of fractional differential equations with improper integral boundary conditions on the half-line

Boundary Value Problems, 2023
This paper investigates the existence of positive solutions for a class of fractional boundary value problems involving an improper integral and the infinite-point on the half-line by making use of properties of the Green function and Avery–Peterson ...
Ning Wang, Zongfu Zhou
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Evaluating Some Improper Sine and Cosine Integrals

Axioms
We consider four infinite collections of improper integrals involving the sine and cosine functions and provide explicit values for the integrals in each of the collections.
Russell A. Gordon
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