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Computing the zeros of cross-product combinations of the Bessel functions with complex order
https://repo.qst.go.jp/records/2001898
https://repo.qst.go.jp/records/2001898d1e1bad8-3c57-4964-a98e-a5f9cffba00c
| アイテムタイプ | 学術雑誌論文 / Journal Article(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2025-10-08 | |||||||||
| タイトル | ||||||||||
| タイトル | Computing the zeros of cross-product combinations of the Bessel functions with complex order | |||||||||
| 言語 | en | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | journal article | |||||||||
| 著者 |
Jeffrey Kershaw
× Jeffrey Kershaw
× Obata Takayuki
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| 抄録 | ||||||||||
| 内容記述タイプ | Abstract | |||||||||
| 内容記述 | The zeros of cross-product combinations of the Bessel functions are often required as the eigenvalues in boundary-value problems with annular or tubular symmetry. Numerical methods to calculate the roots when the order is real have existed for many years, but those methods are unreliable when the order is complex, probably because the distribution of the zeros in the complex plane isunknown. In this work asymptotic expansions for the Bessel cross-product functions are constructed and used to investigate the root distribution in the complex plane for complex order. When the argument of the order is positive (ornegative) the zeros are symmetrically positioned in the first & third (or second & fourth) quadrants of the complex plane. Within a particular quadrant, it is shown that the roots lie on or near to three lines that intersect at a single point. Two of these lines have a finite number of zeros associated with them, while the third line always has an infinite number of roots distributed along it. Approximations to the roots are constructed and used as initial values in an algorithm that more closely estimates the zeros. A longstanding issue with regard to the “exceptional” nature of the lowest root of one of the Bessel cross-product functions when the order is real has also been resolved. | |||||||||
| 書誌情報 |
Results in Applied Mathematics 巻 28, p. 100642, 発行日 2025-10 |
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| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 2590-0374 | |||||||||
| DOI | ||||||||||
| 識別子タイプ | DOI | |||||||||
| 関連識別子 | 10.1016/j.rinam.2025.100642 | |||||||||
