Askey–Wilson polynomials

Askey–Wilson polynomials

In mathematics, the Askey-Wilson polynomials are the polynomials:p_n(x;a,b,c|q) =(ab,ac,ad;q)_na^{-n};_{4}phi_3 left [egin{matrix} q^{-n}&abcdq^{n-1}&ae^{i heta}&ae^{-i heta} \ ab&ac&ad end{matrix} ; q,q ight] where φ is a basic hypergeometric function and "x" = cos(θ) and (,,,)"n" is the q-Pochhammer symbol.

They were introduced by harvtxt|Askey|Wilson|1985 as "q"-analogues of the Wilson polynomials.

References

*Citation | authorlink=Richard Askey | last1=Askey | first1=Richard | last2=Wilson | first2=James | title=Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials | isbn=978-0-8218-2321-7 | id=MathSciNet | id = 783216 | year=1985 | journal=Memoirs of the American Mathematical Society | issn=0065-9266 | volume=54 | issue=319 | pages=iv+55
*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 | id=MathSciNet | id = 2128719 | year=2004 | volume=96


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