Abstract
A family of non-complete orthogonal systems of functions on the ray depending on three real parameters , , is constructed. The elements of this system are piecewise hypergeometric functions with singularity at . For these functions vanish on and the system is reduced to the Jacobi polynomials on the interval . In the general case the functions constructed can be regarded as an interpretation of the expressions . They are eigenfunctions of an exotic Sturm-Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem is found.
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