On Jacobi and continuous Hahn polynomials
Erik Koelink
Abstract
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.
Create a lesson
Related papers
Optimal fractional discrete Hardy inequalities on the half-line
František Štampach, Jakub Waclawek
Capacitary-Distance Hardy Inequality
Yiqun Chen, Jie Xiao, Dachun Yang et al.
Microstructure evolution as a game
Michael Ortiz
Optimal differentiability of isotropic positive definite functions on even-dimensional spheres
Yan Ge
Bilinear Bochner--Riesz Means on the Complex Sphere
S. Bagchi, Md N. Molla, J. Singh et al.
Exact-Support Counterexamples to Euclidean-to-Spherical Transfer of Positive Definiteness in Even Dimensions
Wentao Huang, Haizhang Zhang