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An introduction to second degree forms

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Abstract

We are dealing with orthogonal sequences with respect to forms verifying a second degreee equation, i.e. that its formal Stieltjes functionS(u)(z) satisfies a quadratic equation of the formB(z)S 2(u)(z)+C(z)S(u)(z)+D(z)=0, whereB, C, D are polynomials. Various algebraic properties are given, especially those concerning the quasi-orthogonality of associated sequences.

A classification is outlined. Some examples are quoted. In particular, we give the representation of Tchebychev co-recursive forms for any complex value of the parameter.

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Communicated by C. Brezinski

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Maroni, P. An introduction to second degree forms. Adv Comput Math 3, 59–88 (1995). https://doi.org/10.1007/BF02431996

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  • DOI: https://doi.org/10.1007/BF02431996

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