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| {{distinguish|Al-Salam–Chihara polynomials}}
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| In mathematics, '''Al-Salam–Carlitz polynomials''' ''U''{{su|b=''n''|p=(''a'')}}(''x'';''q'') and ''V''{{su|b=''n''|p=(''a'')}}(''x'';''q'') are two families of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvs|txt|last=Al-Salam|authorlink=Waleed Al-Salam|last2=Carlitz|author2-link=Leonard Carlitz|year=1965}}. {{harvs|txt | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | doi=10.1007/978-3-642-05014-5 | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010|loc=14.24, 14.25}} give a detailed list of their properties.
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| ==Definition==
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| The Al-Salam–Chihara polynomials are given in terms of [[basic hypergeometric function]]s by
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| :<math> U_n^{(a)}(x;q) = (-a)^nq^{n(n-1)/2}{}_2\phi_1(q^{-n}, x^{-1};0;q,qx/a)</math>
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| :<math> V_n^{(a)}(x;q) = (-a)^nq^{-n(n-1)/2}{}_2\phi_0(q^{-n}, x;;q,q^n/a)</math>
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| ==References==
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| *{{Citation | last1=Al-Salam | first1=W. A. | last2=Carlitz | first2=L. | author2-link=Leonard_Carlitz | title=Some orthogonal q-polynomials | doi=10.1002/mana.19650300105 | mr=0197804 | year=1965 | journal=[[Mathematische Nachrichten]] | issn=0025-584X | volume=30 | pages=47–61}}
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| *{{Citation | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}}
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| {{DEFAULTSORT:Al-Salam-Carlitz polynomials}}
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| [[Category:Orthogonal polynomials]]
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Revision as of 06:34, 4 March 2014
7 Courtney Bruno is what folks call me and Really feel comfortable people use the full name. For years he's been living in but now he is considering other options. The job he's been occupying best is a credit authoriser but he's always wanted his own company. To go to karaoke precisely what I do every few. See what's new on my website here: http://www.jurnale.ro/Cum_rezervam_un_bilet_de_avion-e33812-170608.html
Also visit my web blog ... vola.ro bilete avion ieftine