In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky for one of three finite sequences of orthogonal polynomials y. Since they form an orthogonal subset of Routh polynomials it seems consistent to refer to them as Romanovski-Routh polynomials, by analogy with the terms Romanovski-Bessel and Romanovski-Jacobi used by Lesky. As shown by Askey for two other sequencesth is finite sequence orthogonal polynomials of can be expressed in terms of Jacobi polynomials of imaginary argument. In following Raposo et al. they are often referred to simply as Romanovski polynomials.
References
- Lesky, P. A. (1996), "Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen", Z. Angew. Math. Mech., 76 (3): 181–184, Bibcode:1996ZaMM...76..181L, doi:10.1002/zamm.19960760317
- Romanovski, P. A. (1929), "Sur quelques classes nouvelles de polynomes orthogonaux", C. R. Acad. Sci. Paris, 188: 1023
- Routh, E. J. (1884), "On some properties of certain solutions of a differential equation of second order", Proc. London Math. Soc., 16: 245
- Natanson, G. (2015), Exact quantization of the Milson potential via Romanovski-Routh polynomials, arXiv:1310.0796, Bibcode:2013arXiv1310.0796N
- Askey, Richard (1987), "An integral of Ramanujan and orthogonal polynomials", The Journal of the Indian Mathematical Society, New Series, 51: 27–36
- Raposo AP, Weber HJ, Alvarez-Castillo DE, Kirchbach M (2007), "Romanovski polynomials in selected physics problems", Cent. Eur. J. Phys., 5 (3): 253, arXiv:0706.3897, Bibcode:2007CEJPh...5..253R, doi:10.2478/s11534-007-0018-5, S2CID 119120266