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P , n on the segment (0,1). In a general case, our functions can be considered as an interpretation of P , n+. Our functions are solutions of some exotic Sturm-Liouville boundary problem for the hypergeometric differential operator. We find the spectral measure for this problem. 1. Formulation of result Results of the paper are formulated in Subsections 1.1-1.5. Next, in 1.6- 1.9, we discuss existing and hypotetical relations of our phenomenon with some other mathematical topics. 1.1. Jacobi polynomials. Preliminaries. Recall that the Jacobi polynomials P , n are the polynomials on the segment (−1,1) orthogonal with respect to the inner product

Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems