Continuous q-Hahn polynomials explained

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

Definition

The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by ^[1]

	-n
p
	n(x;a,b,c,d\|q)=a

e^-inu(abe^2iu,ac,ad;q)_n{}_4\phi

	-n

	3(q

,abcdq^n-1,ae^i{(t+2u)

},ae^;abe^,ac,ad;q;q)

x=\cos(t+u)

Notes and References

Roelof p433, Springer 2010