- Definition
- References
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 | 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.
Definition
The Al-Salam–Carlitz polynomials are given in terms of basic hypergeometric functions by
References
- {{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}}
- {{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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