J. Korean Math. Soc. 2005; 42(4): 673-693
Printed July 1, 2005
Copyright © The Korean Mathematical Society.
Dong Won Lee
Kyungpook National University
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.
Keywords: orthogonal polynomials, multiple orthogonal polynomials, recurrence relation
MSC numbers: 33C45, 42C05
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