In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky
for one of three finite sequences of
orthogonal polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal
In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...
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
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal
In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...
of can be expressed in terms of
Jacobi polynomials
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P_n^(x)
are a class of Classical orthogonal polynomials, classical orthogonal polynomials. They are orthogonal with respect to the weight
(1-x)^\alpha(1+x)^\beta ...
of imaginary argument. In following Raposo et al.
they are often referred to simply as Romanovski polynomials.
References
{{reflist
Orthogonal polynomials