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Some recurrence relations of multiple orthogonal polynomials
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Abstract
In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d\mu, d\nu)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case
참고문헌 (11)
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- "{\it Recurrence relations in the table of vector orthogonal polynomials}", (nlinear numerical methods and rational approximation ii), pp.61~ (1994)
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