Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems
Journal Article
·
· Sbornik. Mathematics
- Russian Federation State Scientific Center 'A.I. Alikhanov Institute for Theoretical and Experimental Physics', Moscow (Russian Federation)
A family of non-complete orthogonal systems of functions on the ray [0,{infinity}] 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,{infinity}) and the system is reduced to the Jacobi polynomials P{sub n}{sup {alpha}}{sup ,{beta}} on the interval [0,1]. In the general case the functions constructed can be regarded as an interpretation of the expressions P{sub n+{theta}}{sup {alpha}}{sup ,{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.
- OSTI ID:
- 21267019
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 197; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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