General Master Theorems of Integrals with Applications

Mohammad Abu-Ghuwaleh, Rania Saadeh and Ahmad Qazza ()
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Mohammad Abu-Ghuwaleh: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
Rania Saadeh: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan

Mathematics, 2022, vol. 10, issue 19, 1-19

Abstract: 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. The main purpose of this research is to present new fundamental theorems of improper integrals that generate new formulas and tables of integrals. We present six main theorems with associated remarks that can be viewed as generalizations of Cauchy’s results and I.S. Gradshteyn integral tables. Applications to difficult problems are presented that cannot be solved with the usual techniques of residue or contour theorems. The solutions of these applications can be obtained directly, depending on the proposed theorems with an appropriate choice of functions and parameters.

Keywords: improper integrals; power series; analytic function; Cauchy residue theorem; Ramanujan’s principal theorem; integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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