Minimal solutions of three-term recurrence relations and orthogonal polynomials

Author:
Walter Gautschi

Journal:
Math. Comp. **36** (1981), 547-554

MSC:
Primary 33A65; Secondary 65D20, 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606512-6

MathSciNet review:
606512

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Abstract | References | Similar Articles | Additional Information

Abstract: We observe that the well-known recurrence relation for orthogonal polynomials admits a "minimal solution" if *z* is outside the spectrum of the mass distribution with respect to which the polynomials are orthogonal and if the moment problem for this distribution is determined. The minimal solution, indeed is , and can be computed accurately by means of the author's continued fraction algorithm. An application is made to special Gauss-type quadrature formulas.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606512-6

Keywords:
Minimal solutions of three-term recurrence relations,
orthogonal polynomials,
moment problem,
modified moments

Article copyright:
© Copyright 1981
American Mathematical Society