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 

Authors and Corporations:  , , 
In:  Advances in Mathematical Physics, 2009, 2009, p. 143 
Type of Resource:  EArticle 
Language:  Undetermined 
published: 
Hindawi Publishing Corporation

Subjects: 
finc.format 
ElectronicArticle 

finc.mega_collection 
Hindawi Publishing Corporation (CrossRef) 
finc.id 
ai49aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDA5LzI2ODEzNA 
finc.source_id 
49 
ris.type 
EJOUR 
rft.atitle 
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme 
rft.epage 
43 
rft.genre 
article 
rft.issn 
16879120 16879139 
rft.jtitle 
Advances in Mathematical Physics 
rft.tpages 
43 
rft.pages 
143 
rft.pub 
Hindawi Publishing Corporation 
rft.date 
20090101 
x.date 
20090101T00:00:00Z 
rft.spage 
1 
rft.volume 
2009 
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> 
authors 
Array
(
[rft.aulast] => Bruschi
[rft.aufirst] => M.
)
Array ( [rft.aulast] => Calogero [rft.aufirst] => F. ) Array ( [rft.aulast] => Droghei [rft.aufirst] => R. ) 
doi 
10.1155/2009/268134 
languages 
und 
url 
http://dx.doi.org/10.1155/2009/268134 
version 
0.9 
x.subjects 
Physics and Astronomy(all) Applied Mathematics 
x.type 
journalarticle 
x.oa 
1 
openURL 
url_ver=Z39.882004&ctx_ver=Z39.882004&ctx_enc=info%3Aofi%2Fenc%3AUTF8&rfr_id=info%3Asid%2Fwww.hszg.de%3Agenerator&rft.title=Additional+Recursion+Relations%2C+Factorizations%2C+and+Diophantine+Properties+Associated+with+the+Polynomials+of+the+Askey+Scheme&rft.date=20090101&genre=article&issn=16879139&volume=2009&spage=1&epage=43&pages=143&jtitle=Advances+in+Mathematical+Physics&atitle=Additional+Recursion+Relations%2C+Factorizations%2C+and+Diophantine+Properties+Associated+with+the+Polynomials+of+the+Askey+Scheme&aulast=Droghei&aufirst=R.&rft_id=info%3Adoi%2F10.1155%2F2009%2F268134&rft.language%5B0%5D=und 
SOLR  
_version_  1666566971966095373 
access_facet  Electronic Resources 
author  Bruschi, M., Calogero, F., Droghei, R. 
author_sort  bruschi, m. 
branch_nrw  Electronic Resources 
container_start_page  1 
container_title  Advances in Mathematical Physics 
container_volume  2009 
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> 
facet_avail  Online, Free 
finc_class_facet  Physik, Mathematik 
format  ElectronicArticle 
format_de105  Article, EArticle 
format_de14  Article, EArticle 
format_de15  Article, EArticle 
format_de520  Article, EArticle 
format_de540  Article, EArticle 
format_dech1  Article, EArticle 
format_ded117  Article, EArticle 
format_degla1  EArticle 
format_del152  Buch 
format_del189  Article, EArticle 
format_dezi4  Article 
format_dezwi2  Article, EArticle 
format_finc  Article, EArticle 
format_nrw  Article, EArticle 
geogr_code  not assigned 
geogr_code_person  not assigned 
id  ai49aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDA5LzI2ODEzNA 
imprint  Hindawi Publishing Corporation, 2009 
imprint_str_mv  Hindawi Publishing Corporation, 2009 
institution  DEZwi2, DEBrt1, DEGla1, DEZi4, DE15, DE105, DE82, DECh1, DED275, DE14 
issn  16879120, 16879139 
language  Undetermined 
last_indexed  20200513T09:28:36.503Z 
mega_collection  Hindawi Publishing Corporation (CrossRef) 
physical  143 
publishDate  20090101 
publishDateSort  2009 
publisher  Hindawi Publishing Corporation 
recordtype  ai 
score  19,30686 
series  Advances in Mathematical Physics 
source_id  49 
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 