Compatibility of the method of brackets with classical integration rules
The method of brackets is a symbolic approach to the computation of integrals over Rn{{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This article shows that this method is consistent...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-05-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0581 |
| _version_ | 1797659604720549888 |
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| author | Bradshaw Zachary Gonzalez Ivan Jiu Lin Moll Victor Hugo Vignat Christophe |
| author_facet | Bradshaw Zachary Gonzalez Ivan Jiu Lin Moll Victor Hugo Vignat Christophe |
| author_sort | Bradshaw Zachary |
| collection | DOAJ |
| description | The method of brackets is a symbolic approach to the computation of integrals over Rn{{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This article shows that this method is consistent with most classical rules for the computation of integrals, such as the fundamental theorem of calculus, the Laplace transform, the reduction formula for the integration of functions with spherical symmetry, the Cauchy-Schlömilch transformation, and explicit evaluations for multivariate integrals of product of Bessel functions as obtained by Exton and Srivastava. This work is part of a program dedicated to the derivation of solid theoretical grounds for the use of this attractive integration method. |
| first_indexed | 2024-03-11T18:17:34Z |
| format | Article |
| id | doaj.art-d23f2eef1672419b81651dbd759075b2 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-11T18:17:34Z |
| publishDate | 2023-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-d23f2eef1672419b81651dbd759075b22023-10-16T06:06:24ZengDe GruyterOpen Mathematics2391-54552023-05-01211507310.1515/math-2022-0581Compatibility of the method of brackets with classical integration rulesBradshaw Zachary0Gonzalez Ivan1Jiu Lin2Moll Victor Hugo3Vignat Christophe4Department of Mathematics, Tulane University, New Orleans, LA 70118, Louisiana, USAInstituto de Física y Astronomía, Universidad de Valparaiso, Gran Bretaña 1111, Valparaiso, ChileZu Chongzhi Center for Mathematics and Computational Sciences, Duke Kunshan University, Kunshan, Suzhou, Jiangsu Province, ChinaDepartment of Mathematics, Tulane University, New Orleans, LA 70118, Louisiana, USADepartment of Mathematics, Tulane University, New Orleans, LA 70118, Louisiana, USAThe method of brackets is a symbolic approach to the computation of integrals over Rn{{\mathbb{R}}}^{n} based on a deep result by Ramanujan. Its usefulness to obtain new and difficult integrals has been demonstrated many times in the last few years. This article shows that this method is consistent with most classical rules for the computation of integrals, such as the fundamental theorem of calculus, the Laplace transform, the reduction formula for the integration of functions with spherical symmetry, the Cauchy-Schlömilch transformation, and explicit evaluations for multivariate integrals of product of Bessel functions as obtained by Exton and Srivastava. This work is part of a program dedicated to the derivation of solid theoretical grounds for the use of this attractive integration method.https://doi.org/10.1515/math-2022-0581definite integralsmethod of bracketscompatibilityschlömilch transformation33b9933f99 |
| spellingShingle | Bradshaw Zachary Gonzalez Ivan Jiu Lin Moll Victor Hugo Vignat Christophe Compatibility of the method of brackets with classical integration rules Open Mathematics definite integrals method of brackets compatibility schlömilch transformation 33b99 33f99 |
| title | Compatibility of the method of brackets with classical integration rules |
| title_full | Compatibility of the method of brackets with classical integration rules |
| title_fullStr | Compatibility of the method of brackets with classical integration rules |
| title_full_unstemmed | Compatibility of the method of brackets with classical integration rules |
| title_short | Compatibility of the method of brackets with classical integration rules |
| title_sort | compatibility of the method of brackets with classical integration rules |
| topic | definite integrals method of brackets compatibility schlömilch transformation 33b99 33f99 |
| url | https://doi.org/10.1515/math-2022-0581 |
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