Pseudo Jacobi polynomials

In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky[1] for one of three finite sequences of orthogonal polynomials y.[2] Since they form an orthogonal subset of Routh polynomials[3] it seems consistent to refer to them as Romanovski-Routh polynomials,[4] by analogy with the terms Romanovski-Bessel and Romanovski-Jacobi used by Lesky. As shown by Askey [5] 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.[6] they are often referred to simply as Romanovski polynomials.

References
  1. 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
  2. Romanovski, P. A. (1929), "Sur quelques classes nouvelles de polynomes orthogonaux", C. R. Acad. Sci. Paris, 188: 1023
  3. Routh, E. J. (1884), "On some properties of certain solutions of a differential equation of second order", Proc. London Math. Soc., 16: 245
  4. Natanson, G. (2015), Exact quantization of the Milson potential via Romanovski-Routh polynomials, arXiv:1310.0796, Bibcode:2013arXiv1310.0796N
  5. Askey, Richard (1987), "An integral of Ramanujan and orthogonal polynomials", The Journal of the Indian Mathematical Society, New Series, 51: 27–36
  6. 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
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