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Article

A Novel Approach in Solving Improper Integrals

Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
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Author to whom correspondence should be addressed.
Axioms 2022, 11(10), 572; https://doi.org/10.3390/axioms11100572
Submission received: 11 September 2022 / Revised: 3 October 2022 / Accepted: 13 October 2022 / Published: 20 October 2022
(This article belongs to the Special Issue Theory of Functions and Applications)

Abstract

To resolve several challenging applications in many scientific domains, general formulas of improper integrals are provided and established for use in this article. The suggested theorems can be considered generators for new improper integrals with precise solutions, without requiring complex computations. New criteria for handling improper integrals are illustrated in tables to simplify the usage and the applications of the obtained outcomes. The results of this research are compared with those obtained by I.S. Gradshteyn and I.M. Ryzhik in the classical table of integrations. Some well-known theorems on improper integrals are considered to be simple cases in the context of our work. Some applications related to finding Green’s function, one-dimensional vibrating string problems, wave motion in elastic solids, and computing Fourier transforms are presented.
Keywords: improper integrals; power series; analytic function; Cauchy residue theorem; Ramanujan’s master theorem improper integrals; power series; analytic function; Cauchy residue theorem; Ramanujan’s master theorem

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MDPI and ACS Style

Abu-Ghuwaleh, M.; Saadeh, R.; Qazza, A. A Novel Approach in Solving Improper Integrals. Axioms 2022, 11, 572. https://doi.org/10.3390/axioms11100572

AMA Style

Abu-Ghuwaleh M, Saadeh R, Qazza A. A Novel Approach in Solving Improper Integrals. Axioms. 2022; 11(10):572. https://doi.org/10.3390/axioms11100572

Chicago/Turabian Style

Abu-Ghuwaleh, Mohammad, Rania Saadeh, and Ahmad Qazza. 2022. "A Novel Approach in Solving Improper Integrals" Axioms 11, no. 10: 572. https://doi.org/10.3390/axioms11100572

APA Style

Abu-Ghuwaleh, M., Saadeh, R., & Qazza, A. (2022). A Novel Approach in Solving Improper Integrals. Axioms, 11(10), 572. https://doi.org/10.3390/axioms11100572

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