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 threeterm recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a...
Journal Title:  Advances in Mathematical Physics 

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In:  Advances in Mathematical Physics, 2009, 2009, p. 143 
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Hindawi Publishing Corporation

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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 threeterm 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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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 threeterm 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. 16879120 16879139 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 threeterm 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 