On Radial Distribution and Quasi-exact Solvability of Brioschi-Halphen Equation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911333377638400 |
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| author | Idiong, U. S. Bassey, U. N. Obabiyi, O. S. |
| author_facet | Idiong, U. S. Bassey, U. N. Obabiyi, O. S. |
| contents | The Brioschi-Halphen equation (BHE) is a second order complex differential equation obtained by a two step transformation of the Lamé equation. The Lamé equation is an equation in Astronomical physics used in the study of motion of planetary bodies. In this seminar, the radial part of the BHE for sufficiently large $r$ and the argument limit $2π$ is obtained. The asymptotic radial wave function associated with BHE is obtained in terms of canonical polynomials $\mathscr{P}_{n+1},$ and spherical function in $L^{2}(G,{\rm d}μ), G=SL(2,\mathbb{R})$ using point canonical transformation and distributional solution in $\mathscr{C}_{c}^{\infty}(Ω)$ using Fourier transform method are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Radial Distribution and Quasi-exact Solvability of Brioschi-Halphen Equation Idiong, U. S. Bassey, U. N. Obabiyi, O. S. Classical Analysis and ODEs Mathematical Physics Functional Analysis 2020: 46F10, 16S30 The Brioschi-Halphen equation (BHE) is a second order complex differential equation obtained by a two step transformation of the Lamé equation. The Lamé equation is an equation in Astronomical physics used in the study of motion of planetary bodies. In this seminar, the radial part of the BHE for sufficiently large $r$ and the argument limit $2π$ is obtained. The asymptotic radial wave function associated with BHE is obtained in terms of canonical polynomials $\mathscr{P}_{n+1},$ and spherical function in $L^{2}(G,{\rm d}μ), G=SL(2,\mathbb{R})$ using point canonical transformation and distributional solution in $\mathscr{C}_{c}^{\infty}(Ω)$ using Fourier transform method are obtained. |
| title | On Radial Distribution and Quasi-exact Solvability of Brioschi-Halphen Equation |
| topic | Classical Analysis and ODEs Mathematical Physics Functional Analysis 2020: 46F10, 16S30 |
| url | https://arxiv.org/abs/2512.19751 |