2019
DOI: 10.1080/10236198.2019.1627346
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Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice

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Cited by 12 publications
(7 citation statements)
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“…These programs were designed for older versions of maple and do not handle all orthogonal polynomials in the Askey table. Recently Tcheutia [14] extended the Maple implementation of retode to cover classical orthogonal polynomials on quadratic and q-quadratic lattices and was able to identify the second family (1.2) as Wilson polynomials, confirming the analysis in Section 3.…”
Section: Introductionsupporting
confidence: 61%
“…These programs were designed for older versions of maple and do not handle all orthogonal polynomials in the Askey table. Recently Tcheutia [14] extended the Maple implementation of retode to cover classical orthogonal polynomials on quadratic and q-quadratic lattices and was able to identify the second family (1.2) as Wilson polynomials, confirming the analysis in Section 3.…”
Section: Introductionsupporting
confidence: 61%
“…Since the labeling of orthogonal polynomials in the (q-)Askey scheme is by the sequences x k , h k , g k or by the parameters occurring in their expansions is so clean, these data may be helpful for recognizing polynomials in these schemes from the coefficients in the three-term recurrence relation, assuming that it would be possible to obtain these data from these coefficients. See Tcheutia [14] for recent work on this recognition problem by different methods.…”
Section: Further Perspectivesmentioning
confidence: 99%
“…3c. big q-Laguerre (11), q −1 -Meixner ( 13), affine q-Krawtchouk (16), quantum q −1 -Krawtchouk (14)…”
Section: Introductionunclassified
“…, where   Substituting the value of  in terms of the energy from Eq. (19a), the PPS formula (24) could be inverted to give the following energy spectrum formula…”
Section: 8mentioning
confidence: 99%
“…are not yet known. This is still an open problem in orthogonal polynomials [21,23,24]. Nonetheless, it is conjectured that ( , ) ( ; , )…”
Section: 12mentioning
confidence: 99%