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Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polyn...

<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...

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Journal Title: Advances in Mathematical Physics
Authors and Corporations: Bruschi, M., Calogero, F., Droghei, R.
In: Advances in Mathematical Physics, 2009, 2009, p. 1-43
Type of Resource: E-Article
Language: Undetermined
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Hindawi Publishing Corporation
Subjects:
Physics and Astronomy(all)
Applied Mathematics
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rft.atitle Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
rft.epage 43
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abstract <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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doi 10.1155/2009/268134
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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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spellingBruschi, M. Calogero, F. Droghei, R. 1687-9120 1687-9139 Hindawi Publishing Corporation Physics and Astronomy(all) Applied Mathematics 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
spellingShingleBruschi, M., Calogero, F., Droghei, R., Advances in Mathematical Physics, Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme, Physics and Astronomy(all), Applied Mathematics
titleAdditional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
title_fullAdditional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
title_fullStrAdditional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
title_full_unstemmedAdditional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
title_shortAdditional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
title_sortadditional recursion relations, factorizations, and diophantine properties associated with the polynomials of the askey scheme
topicPhysics and Astronomy(all), Applied Mathematics
urlhttp://dx.doi.org/10.1155/2009/268134