Continuous q-Hahn polynomials

The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by Roelof p433, Springer 2010

:$p\_n(x;a,b,c,d|q)=a^\{-n\}e^\{-inu\}(abe^\{2iu\},ac,ad;q)\_n\{\}\_4\backslash phi\_3(q^\{-n\},abcdq^\{n-1\},ae^\{i\{(t+2u)\}\},ae^\{-it\};abe^\{2iu\},ac,ad;q;q)$

$x=\backslash cos(t+u)$

File:CONTINUOUS q hahn ABS COMPLEX3D Maple PLOT.gif |File:CONTINUOUS q hahn IIM COMPLEX3D Maple PLOT.gif |File:CONTINUOUS q hahn RE COMPLEX3D Maple PLOT.gif

File:CONTINUOUS q hahn ABS densitu Maple PLOT.gif |File:CONTINUOUS q hahn im densitu Maple PLOT.gif |File:CONTINUOUS q hahn RE densitu Maple PLOT.gif

{{Reflist}}

• {{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 | 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=Chapter 18: Orthogonal Polynomials|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}

Category:Orthogonal polynomials

Category:Q-analogs

Category:Special hypergeometric functions