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In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation
When p is a non-negative integer, it has polynomial solutions called Ince polynomials. In particular, when , then it has a closed-form solution[1]
where is a constant.
See also
References
- ^ Cheung, Tsz Yung. "Liouvillian solutions of Whittaker-Ince equation". Journal of Symbolic Computation. 115 (March-April 2023): 18–38. doi:10.1016/j.jsc.2022.07.002.
- Boyer, C. P.; Kalnins, E. G.; Miller, W. Jr. (1975), "Lie theory and separation of variables. VII. The harmonic oscillator in elliptic coordinates and Ince polynomials" (PDF), Journal of Mathematical Physics, 16 (3): 512–517, Bibcode:1975JMP....16..512B, doi:10.1063/1.522574, hdl:10289/1243, ISSN 0022-2488, MR 0372384
- Magnus, Wilhelm; Winkler, Stanley (1966), Hill's equation, Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons\, New York-London-Sydney, ISBN 978-0-486-49565-1, MR 0197830
- Mennicken, Reinhard (1968), "On Ince's equation", Archive for Rational Mechanics and Analysis, 29 (2), Springer Berlin / Heidelberg: 144–160, Bibcode:1968ArRMA..29..144M, doi:10.1007/BF00281363, ISSN 0003-9527, MR 0223636, S2CID 122886716
- Wolf, G. (2010), "Equations of Whittaker–Hill and Ince", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
