“Q-Hahn polynomials”的意思、由来-开放百科全书

词条

Q-Hahn polynomials

释义

Definition
Orthogonality
Recurrence and difference relations
Rodrigues formula
Generating function
Relation to other polynomials
References

{{see also|continuous q-Hahn polynomials|dual q-Hahn polynomials|continuous dual q-Hahn polynomials}}{{DISPLAYTITLE: q-Hahn polynomials}}

In mathematics, the q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. {{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}} give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by

Orthogonality

Recurrence and difference relations

Rodrigues formula

Generating function

Relation to other polynomials

q-Hahn polynomials→ Quantum q-Krawtchouk polynomials：

q-Hahn polynomials→ Hahn polynomials

make the substitution, into definition of q-Hahn polynomials, and find the limit q→1, we obtain

：

，which is exactly Hahn polynomials.

References

{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=Cambridge University Press | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 | mr=2128719 | year=2004 | volume=96}}
{{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}}
{{dlmf|id=18|title=|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}
{{cite journal|last1=Costas-Santos|first1=R.S.|last2=Sánchez-Lara|first2=J.F.|title=Orthogonality of q-polynomials for non-standard parameters|journal=Journal of Approximation Theory|date=September 2011|volume=163|issue=9|pages=1246–1268|doi=10.1016/j.jat.2011.04.005}}

3 : Orthogonal polynomials|Q-analogs|Special hypergeometric functions

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