Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
The spheroidal harmonics Slm(θ;c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical...
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| Format: | Article |
| Language: | English |
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Elsevier
2015-06-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269315003731 |
| _version_ | 1830220810398203904 |
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| author | Shahar Hod |
| author_facet | Shahar Hod |
| author_sort | Shahar Hod |
| collection | DOAJ |
| description | The spheroidal harmonics Slm(θ;c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm(c)} of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m→∞ with a fixed value of c, or to the complementary regime |c|→∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m→∞ and |c|→∞ with a fixed m/c ratio. |
| first_indexed | 2024-12-18T08:11:56Z |
| format | Article |
| id | doaj.art-cd55f54dc8564ec4be98f0372bfe20b9 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-18T08:11:56Z |
| publishDate | 2015-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-cd55f54dc8564ec4be98f0372bfe20b92022-12-21T21:14:52ZengElsevierPhysics Letters B0370-26932015-06-01746365367Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysisShahar Hod0The Ruppin Academic Center, Emeq Hefer 40250, Israel; The Hadassah Institute, Jerusalem 91010, Israel; Correspondence to: The Ruppin Academic Center, Emeq Hefer 40250, Israel.The spheroidal harmonics Slm(θ;c) have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena, including black-hole perturbation theory and wave scattering by nonspherical objects. The asymptotic eigenvalues {Alm(c)} of these functions have been determined by many authors. However, it should be emphasized that all the previous asymptotic analyzes were restricted either to the regime m→∞ with a fixed value of c, or to the complementary regime |c|→∞ with a fixed value of m. A fuller understanding of the asymptotic behavior of the eigenvalue spectrum requires an analysis which is asymptotically uniform in both m and c. In this paper we analyze the asymptotic eigenvalue spectrum of these important functions in the double limit m→∞ and |c|→∞ with a fixed m/c ratio.http://www.sciencedirect.com/science/article/pii/S0370269315003731 |
| spellingShingle | Shahar Hod Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis Physics Letters B |
| title | Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis |
| title_full | Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis |
| title_fullStr | Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis |
| title_full_unstemmed | Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis |
| title_short | Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis |
| title_sort | eigenvalue spectrum of the spheroidal harmonics a uniform asymptotic analysis |
| url | http://www.sciencedirect.com/science/article/pii/S0370269315003731 |
| work_keys_str_mv | AT shaharhod eigenvaluespectrumofthespheroidalharmonicsauniformasymptoticanalysis |