Pseudo Jacobi polynomials

In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky{{Citation |last1 = Lesky|first1 = P. A.|title = Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen|year = 1996|journal = Z. Angew. Math. Mech. |volume = 76|issue = 3|pages = 181–184|bibcode = 1996ZaMM...76..181L|doi = 10.1002/zamm.19960760317}} for one of three finite sequences of orthogonal polynomials y.{{Citation |last1 = Romanovski|first1 = P. A.|title = Sur quelques classes nouvelles de polynomes orthogonaux|year = 1929|journal = C. R. Acad. Sci. Paris|volume = 188|pages = 1023}} Since they form an orthogonal subset of Routh polynomials{{Citation |last1 = Routh|first1 = E. J. |title = On some properties of certain solutions of a differential equation of second order|year = 1884|journal = Proc. London Math. Soc. |volume = 16|pages = 245}} it seems consistent to refer to them as Romanovski-Routh polynomials,{{citation |last1 = Natanson|first1 = G. |title = Exact quantization of the Milson potential via Romanovski-Routh polynomials|year = 2015|arxiv=1310.0796 |bibcode = 2013arXiv1310.0796N}} by analogy with the terms Romanovski-Bessel and Romanovski-Jacobi used by Lesky. As shown by Askey {{Citation | last1=Askey | first1=Richard | title=An integral of Ramanujan and orthogonal polynomials | year=1987 | journal=The Journal of the Indian Mathematical Society |series=New Series | volume=51 | pages=27–36}} 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.{{Citation |vauthors=Raposo AP, Weber HJ, Alvarez-Castillo DE, Kirchbach M | title=Romanovski polynomials in selected physics problems| year=2007 | journal=Cent. Eur. J. Phys. | volume=5 | issue=3| pages=253| doi=10.2478/s11534-007-0018-5| arxiv=0706.3897| bibcode=2007CEJPh...5..253R| s2cid=119120266}} they are often referred to simply as Romanovski polynomials.