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Alternative orthogonal polynomials and quadratures. (English) Zbl 1107.33006

Summary: A bidirectional orthogonalization algorithm is applied to construct sequenes of polynomials, which are orthogonal over the interval \([0,1]\) with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of inverse orthogonalization procedure. Quadratures, generating by the sequences, are described. An example on approximation of the Cauchy problem is given.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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