Infinite Series Based on Bessel Zeros
An interesting series based on Bessel function roots (zeros) is discussed and numerically analyzed. The novel-derived simplified general solutions are based on Lommel polynomials. This kind of series can have a large practical use in many scientific areas, such as solid mechanics, fluid mechanics, t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/23/12932 |
| _version_ | 1797400367058649088 |
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| author | Kamil Urbanowicz |
| author_facet | Kamil Urbanowicz |
| author_sort | Kamil Urbanowicz |
| collection | DOAJ |
| description | An interesting series based on Bessel function roots (zeros) is discussed and numerically analyzed. The novel-derived simplified general solutions are based on Lommel polynomials. This kind of series can have a large practical use in many scientific areas, such as solid mechanics, fluid mechanics, thermodynamics, electronics, physics, etc. Some practical examples connected with fluid mechanics are provided in this paper. The errors in Afanasiev solutions are corrected. In addition, the main solution for the series analyzed by Baricz and Angel is presented. |
| first_indexed | 2024-03-09T01:54:35Z |
| format | Article |
| id | doaj.art-2a2aa1f806b74b1aaaccc65f5062e9da |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T01:54:35Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2a2aa1f806b74b1aaaccc65f5062e9da2023-12-08T15:12:12ZengMDPI AGApplied Sciences2076-34172023-12-0113231293210.3390/app132312932Infinite Series Based on Bessel ZerosKamil Urbanowicz0Faculty of Mechanical Engineering and Mechatronics, West Pomeranian University of Technology in Szczecin, 70-310 Szczecin, PolandAn interesting series based on Bessel function roots (zeros) is discussed and numerically analyzed. The novel-derived simplified general solutions are based on Lommel polynomials. This kind of series can have a large practical use in many scientific areas, such as solid mechanics, fluid mechanics, thermodynamics, electronics, physics, etc. Some practical examples connected with fluid mechanics are provided in this paper. The errors in Afanasiev solutions are corrected. In addition, the main solution for the series analyzed by Baricz and Angel is presented.https://www.mdpi.com/2076-3417/13/23/12932Bessel functionsrootszerosinfinite seriesLommel polynomialRayleigh sums |
| spellingShingle | Kamil Urbanowicz Infinite Series Based on Bessel Zeros Applied Sciences Bessel functions roots zeros infinite series Lommel polynomial Rayleigh sums |
| title | Infinite Series Based on Bessel Zeros |
| title_full | Infinite Series Based on Bessel Zeros |
| title_fullStr | Infinite Series Based on Bessel Zeros |
| title_full_unstemmed | Infinite Series Based on Bessel Zeros |
| title_short | Infinite Series Based on Bessel Zeros |
| title_sort | infinite series based on bessel zeros |
| topic | Bessel functions roots zeros infinite series Lommel polynomial Rayleigh sums |
| url | https://www.mdpi.com/2076-3417/13/23/12932 |
| work_keys_str_mv | AT kamilurbanowicz infiniteseriesbasedonbesselzeros |