Staff View: Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

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...

Bibliographic Details
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
published:	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
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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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spelling	Bruschi, 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
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, Physics and Astronomy(all), Applied Mathematics
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
topic	Physics and Astronomy(all), Applied Mathematics
url	http://dx.doi.org/10.1155/2009/268134