Any orthogonal polynomial family defined by Favard's theorem satisfies Q_{p+s}(x)=M(x)Q_p(x)+N(x)Q_{p-t}(x), with coefficients built from the standard recurrence coefficients.
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Three-term Recurrence Relation with Arbitrary Degree Steps for Orthogonal Polynomials
Any orthogonal polynomial family defined by Favard's theorem satisfies Q_{p+s}(x)=M(x)Q_p(x)+N(x)Q_{p-t}(x), with coefficients built from the standard recurrence coefficients.