Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using Casorati determinants of Hahn polynomials (hnα,β,N)n,  construct for each pair F=(F1,F2)F=(F1,F2) of finite sets of positive integers polynomials hnα,β,N;F, n∈σFn∈σF, which are eigenfunctions of a second order difference operator, where σFσF is certain set of nonnegative integers, σF⊊︀NσF⊊︀N. When N∈NN∈N and αα, ββ, NN and FF satisfy a suitable admissibility condition,  prove that the polynomials hnα,β,N;F are also orthogonal and complete with respect to a positive measure (exceptional Hahn polynomials). By passing to the limit,  transform the Casorati determinant of Hahn polynomials into a Wronskian type determinant of Jacobi polynomials (Pnα,β)n. Under suitable conditions for αα, ββ and FF, these Wronskian type determinants turn out to be exceptional Jacobi polynomials.
['Antonio J. Durán']
I am writing a research paper on a idea Exceptional Hahn and Jacobi orthogonal polynomials
[{"from": "human", "value": "I am writing a research paper on a idea Exceptional Hahn and Jacobi orthogonal polynomials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using Casorati determinants of Hahn polynomials (hn\u03b1,\u03b2,N)n,  construct for each pair F=(F1,F2)F=(F1,F2) of finite sets of positive integers polynomials hn\u03b1,\u03b2,N;F, n\u2208\u03c3Fn\u2208\u03c3F, which are eigenfunctions of a second order difference operator, where \u03c3F\u03c3F is certain set of nonnegative integers, \u03c3F\u228a\ufe00N\u03c3F\u228a\ufe00N. When N\u2208NN\u2208N and \u03b1\u03b1, \u03b2\u03b2, NN and FF satisfy a suitable admissibility condition,  prove that the polynomials hn\u03b1,\u03b2,N;F are also orthogonal and complete with respect to a positive measure (exceptional Hahn polynomials). By passing to the limit,  transform the Casorati determinant of Hahn polynomials into a Wronskian type determinant of Jacobi polynomials (Pn\u03b1,\u03b2)n. Under suitable conditions for \u03b1\u03b1, \u03b2\u03b2 and FF, these Wronskian type determinants turn out to be exceptional Jacobi polynomials."}]