Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order
The paper presents the derivation of the asymptotic behavior of -zeros of the modified Bessel function of imaginary order Kᵢᵥ(). This derivation is based on the quasiclassical treatment of the exponential potential on the positive half-axis. The asymptotic expression for the -zeros (zeros with respe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211366 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order. Yuri Krynytskyi and Andrij Rovenchak. SIGMA 17 (2021), 057, 7 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708461045809152 |
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| author | Krynytskyi, Yuri Rovenchak, Andrij |
| author_facet | Krynytskyi, Yuri Rovenchak, Andrij |
| citation_txt | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order. Yuri Krynytskyi and Andrij Rovenchak. SIGMA 17 (2021), 057, 7 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The paper presents the derivation of the asymptotic behavior of -zeros of the modified Bessel function of imaginary order Kᵢᵥ(). This derivation is based on the quasiclassical treatment of the exponential potential on the positive half-axis. The asymptotic expression for the -zeros (zeros with respect to order) contains the Lambert function, which is readily available in most computer algebra systems and numerical software packages. The use of this function provides much higher accuracy of the estimation compared to known relations containing the logarithm, which is just the leading term of () at large . Our result ensures accuracy sufficient for practical applications.
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| first_indexed | 2026-03-19T06:50:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211366 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T06:50:25Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Krynytskyi, Yuri Rovenchak, Andrij 2025-12-30T15:57:13Z 2021 Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order. Yuri Krynytskyi and Andrij Rovenchak. SIGMA 17 (2021), 057, 7 pages 1815-0659 2020 Mathematics Subject Classification: 33C10; 81Q05; 81Q20 arXiv:2103.01732 https://nasplib.isofts.kiev.ua/handle/123456789/211366 https://doi.org/10.3842/SIGMA.2021.057 The paper presents the derivation of the asymptotic behavior of -zeros of the modified Bessel function of imaginary order Kᵢᵥ(). This derivation is based on the quasiclassical treatment of the exponential potential on the positive half-axis. The asymptotic expression for the -zeros (zeros with respect to order) contains the Lambert function, which is readily available in most computer algebra systems and numerical software packages. The use of this function provides much higher accuracy of the estimation compared to known relations containing the logarithm, which is just the leading term of () at large . Our result ensures accuracy sufficient for practical applications. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order Article published earlier |
| spellingShingle | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order Krynytskyi, Yuri Rovenchak, Andrij |
| title | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order |
| title_full | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order |
| title_fullStr | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order |
| title_full_unstemmed | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order |
| title_short | Asymptotic Estimation for Eigenvalues in the Exponential Potential and for Zeros of Kᵢᵥ() with Respect to Order |
| title_sort | asymptotic estimation for eigenvalues in the exponential potential and for zeros of kᵢᵥ() with respect to order |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211366 |
| work_keys_str_mv | AT krynytskyiyuri asymptoticestimationforeigenvaluesintheexponentialpotentialandforzerosofkivwithrespecttoorder AT rovenchakandrij asymptoticestimationforeigenvaluesintheexponentialpotentialandforzerosofkivwithrespecttoorder |