Division problem of a regular form: the case \(x^2u=\lambda xv\) (Q554840)
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scientific article; zbMATH DE number 5930225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Division problem of a regular form: the case \(x^2u=\lambda xv\) |
scientific article; zbMATH DE number 5930225 |
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Division problem of a regular form: the case \(x^2u=\lambda xv\) (English)
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22 July 2011
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Summary: We present a systematic study of a regular linear functional \(v\) to find all regular forms \(u\) which satisfy the equation \(x^{2}u = \lambda xv\), \(\lambda \in \mathbb C - \{ 0 \}\). We also give the second-order recurrence relation of the orthogonal polynomial sequence with respect to \(u\) and study the semiclassical character of the found families. We conclude by treating some examples.
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second-order recurrence relation
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orthogonal polynomial sequence
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