Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula. In a special case this relation dates back to work by Bateman in 1933 and we follow a part of the historical development for these polynomials. Some applications of this relation are given.
Change of Basis between Classical Orthogonal Polynomials
Asymptotic approximations of the continuous Hahn polynomials and their zeros
Asymptotic expansions of Jacobi polynomials for large values of $β$ and of their zeros
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