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Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
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| Zeitschriftentitel: | Advances in Mathematical Physics |
|---|---|
| Personen und Körperschaften: | , , |
| In: | Advances in Mathematical Physics, 2009, 2009, S. 1-43 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Hindawi Limited
|
| Schlagwörter: |
| author_facet |
Bruschi, M. Calogero, F. Droghei, R. Bruschi, M. Calogero, F. Droghei, R. |
|---|---|
| author |
Bruschi, M. Calogero, F. Droghei, R. |
| spellingShingle |
Bruschi, M. Calogero, F. Droghei, R. Advances in Mathematical Physics Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme Applied Mathematics General Physics and Astronomy |
| author_sort |
bruschi, m. |
| spelling |
Bruschi, M. Calogero, F. Droghei, R. 1687-9120 1687-9139 Hindawi Limited Applied Mathematics General Physics and Astronomy http://dx.doi.org/10.1155/2009/268134 <jats:p>In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms of<jats:italic>integers</jats:italic>(<jats:italic>Diophantine</jats:italic>relations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.</jats:p> Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme Advances in Mathematical Physics |
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| title |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_unstemmed |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_full |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_fullStr |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_full_unstemmed |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_short |
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_sort |
additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the askey scheme |
| topic |
Applied Mathematics General Physics and Astronomy |
| url |
http://dx.doi.org/10.1155/2009/268134 |
| publishDate |
2009 |
| physical |
1-43 |
| description |
<jats:p>In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms of<jats:italic>integers</jats:italic>(<jats:italic>Diophantine</jats:italic>relations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.</jats:p> |
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| author | Bruschi, M., Calogero, F., Droghei, R. |
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| container_title | Advances in Mathematical Physics |
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| description | <jats:p>In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms of<jats:italic>integers</jats:italic>(<jats:italic>Diophantine</jats:italic>relations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.</jats:p> |
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| spelling | Bruschi, M. Calogero, F. Droghei, R. 1687-9120 1687-9139 Hindawi Limited Applied Mathematics General Physics and Astronomy http://dx.doi.org/10.1155/2009/268134 <jats:p>In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three-term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of these polynomials characterized by special values of their parameters, factorizations are identified yielding some or all of their zeros—generally given by simple expressions in terms of<jats:italic>integers</jats:italic>(<jats:italic>Diophantine</jats:italic>relations). The factorization findings generally are applicable for values of the Askey polynomials that extend beyond those for which the standard orthogonality relations hold. Most of these results are not (yet) reported in the standard compilations.</jats:p> Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme Advances in Mathematical Physics |
| spellingShingle | Bruschi, M., Calogero, F., Droghei, R., Advances in Mathematical Physics, Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme, Applied Mathematics, General Physics and Astronomy |
| title | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_full | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_fullStr | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_full_unstemmed | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_short | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| title_sort | additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the askey scheme |
| title_unstemmed | Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme |
| topic | Applied Mathematics, General Physics and Astronomy |
| url | http://dx.doi.org/10.1155/2009/268134 |