On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle
Keyword(s):
In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.
2007 ◽
Vol 148
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pp. 35-48
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1955 ◽
Vol 78
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pp. 492-492
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Keyword(s):
1982 ◽
Vol 25
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pp. 291-295
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1998 ◽
Vol 28
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pp. 547-594
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2002 ◽
pp. 237-260
1983 ◽
Vol 26
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pp. 410-417
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2011 ◽
Vol 57
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pp. 409-416
2015 ◽
Vol 36
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pp. 930-941