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Zbl 0938.33006
Volkmer, H.
Expansions in products of Heine-Stieltjes polynomials. (English)
[J] Constructive Approximation 15, No.4, 467-480 (1999). ISSN 0176-4276; ISSN 1432-0940/e

Polynomial Heine-Stieltjes solutions $E_n$ of the Fuchsian differential equation $$E''+\sum^k_{j=0} {\rho_j\over s-a_j}E'+{\sum^{k-1}_{i=0} \lambda_is^i \over\prod^k_{j=0} (s-a_j)}E=0$$ were studied. The existence and uniqueness theorem forms the basis of the study. Orthogonality of the polynomial products $E_n(S_1) E_n(S_2) \dots E_n(S_k)$ and corresponding expansions were investigated. These products lead to homogeneous polynomial solutions of a partial differential equation, these polynomials also have orthogonality properties. An expansion of analytic functions in terms of the above products was proved.
[Váslaw Burjan (Praha)]

MSC 2000:: *33C50 Hypergeometric functions and integrals in several variables
41A10 Approximation by polynomials

Keywords: orthogonal polynomials; Heine-Stieltjes polynomials

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