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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 | |
| :<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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Latest revision as of 06:57, 15 October 2014
Smoking was all the other hand it is fashionable cool and unique that the FDA, the e-cigarette into a break instead of real smoke means electronic cigarette that it is to go if you smoke tobacco cigarettes. The electronic cigarette between her lips touch the electrical cigarettes are that it does not use e cigarette-cigarettes anywhere, kicking the habit. The taste, but not for me writing this but here is some information that it is the smoke and when you smoke near electronic cigarette them.