Some new results for chain-sequence polynomials


Doorn, Erik A. van (1995) Some new results for chain-sequence polynomials. Journal of Computational and Applied Mathematics, 57 (1-2). pp. 309-317. ISSN 0377-0427

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Abstract:We study the class of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying a recurrence relation of the type Pn(x) = (x − cn)Pn−1(x) − λnPn−2(x), n> 1, where λn ≠ 0 and the sequence {λn+1/(cncn+1)}n=1∞ constitutes a chain sequence. We obtain a new characterization of in terms of the moment sequence associated with an orthogonal polynomial sequence, and contribute to the solution of the problem of determining a (signed) orthogonalizing measure for a member of C.

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Copyright:© 1995 Elsevier Science
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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