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Mat. Sb., 2006, Volume 197, Number 11, Pages 51–78 (Mi msb1146)  

Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems

Yu. A. Neretinab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b University of Vienna

Abstract: A family of non-complete orthogonal systems of functions on the ray $[0,\infty]$ depending on three real parameters $\alpha$, $\beta$$\theta$ is constructed. The elements of this system are piecewise hypergeometric functions with singularity at $x=1$. For $\theta=0$ these functions vanish on $[1,\infty)$ and the system is reduced to the Jacobi polynomials $P_n^{\alpha,\beta}$ on the interval $[0,1]$. In the general case the functions constructed can be regarded as an interpretation of the expressions $P_{n+\theta}^{\alpha,\beta}$. They are eigenfunctions of an exotic Sturm–Liouville boundary-value problem for the hypergeometric differential operator. The spectral measure for this problem is found.
Bibliography: 27 titles.

DOI: https://doi.org/10.4213/sm1146

Full text: PDF file (739 kB)
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English version:
Sbornik: Mathematics, 2006, 197:11, 1607–1633

Bibliographic databases:

UDC: 512.763
MSC: Primary 33C45; Secondary 42C05
Received: 07.09.2005 and 22.03.2006

Citation: Yu. A. Neretin, “Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems”, Mat. Sb., 197:11 (2006), 51–78; Sb. Math., 197:11 (2006), 1607–1633

Citation in format AMSBIB
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