Pseudo Jacobi polynomials
From HandWiki
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
- ↑ Lesky, P. A. (1996), "Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen", Z. Angew. Math. Mech. 76 (3): 181–184, doi:10.1002/zamm.19960760317, Bibcode: 1996ZaMM...76..181L
- ↑ 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, 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
- ↑ "Romanovski polynomials in selected physics problems", Cent. Eur. J. Phys. 5 (3): 253, 2007, doi:10.2478/s11534-007-0018-5, Bibcode: 2007CEJPh...5..253R
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