General Master Theorems of Integrals with Applications
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3547 |
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| author | Mohammad Abu-Ghuwaleh Rania Saadeh Ahmad Qazza |
| author_facet | Mohammad Abu-Ghuwaleh Rania Saadeh Ahmad Qazza |
| author_sort | Mohammad Abu-Ghuwaleh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T21:28:09Z |
| format | Article |
| id | doaj.art-05c8c16008334610819132ebb705d0d8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:28:09Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-05c8c16008334610819132ebb705d0d82023-11-23T21:03:24ZengMDPI AGMathematics2227-73902022-09-011019354710.3390/math10193547General Master Theorems of Integrals with ApplicationsMohammad Abu-Ghuwaleh0Rania Saadeh1Ahmad Qazza2Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, JordanDepartment of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, JordanDepartment of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, JordanMany 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.https://www.mdpi.com/2227-7390/10/19/3547improper integralspower seriesanalytic functionCauchy residue theoremRamanujan’s principal theoremintegral equation |
| spellingShingle | Mohammad Abu-Ghuwaleh Rania Saadeh Ahmad Qazza General Master Theorems of Integrals with Applications Mathematics improper integrals power series analytic function Cauchy residue theorem Ramanujan’s principal theorem integral equation |
| title | General Master Theorems of Integrals with Applications |
| title_full | General Master Theorems of Integrals with Applications |
| title_fullStr | General Master Theorems of Integrals with Applications |
| title_full_unstemmed | General Master Theorems of Integrals with Applications |
| title_short | General Master Theorems of Integrals with Applications |
| title_sort | general master theorems of integrals with applications |
| topic | improper integrals power series analytic function Cauchy residue theorem Ramanujan’s principal theorem integral equation |
| url | https://www.mdpi.com/2227-7390/10/19/3547 |
| work_keys_str_mv | AT mohammadabughuwaleh generalmastertheoremsofintegralswithapplications AT raniasaadeh generalmastertheoremsofintegralswithapplications AT ahmadqazza generalmastertheoremsofintegralswithapplications |