Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systemsстатья
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Дата последнего поиска статьи во внешних источниках: 8 декабря 2019 г.
Аннотация:A family of non-complete orthogonal systems of functions on the ray [0,∞] depending on three real parameters α, β, θ is constructed. The elements of this system are piecewise hypergeometric functions with singularity at x=1. For θ=0 these functions vanish on [1,∞) and the system is reduced to the Jacobi polynomials P_{α,β}^n on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P_}α,β}^{n+θ}. They are eigenfunctions of an exotic Sturm–Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem is found.