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: 181
  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
  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 A P, Weber H J, Alvarez-Castillo D E and Kirchbach M (2007), "Romanovski polynomials in selected physics problems", Centr. Eur. J. Phys. 5: 253
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