Orthogonal polynomials associated with weighting function
 |  |  |
(1)
|
 |  |  |
(2)
|
for 
and 
.
Defining
![q=exp[-(2k^2)^(-1)],](/images/equations/Stieltjes-WigertPolynomial/NumberedEquation1.svg) |
(3)
|
then
 |  |  |
(4)
|
 |  | ![((-1)^nq^(n/2+1/4))/(sqrt((q;q)_n))sum_(nu=0)^(n)[n; nu]q^(nu^2)(-sqrt(q)x)^nu,](/images/equations/Stieltjes-WigertPolynomial/Inline14.svg) |
(5)
|
where 
is a q-Pochhammer symbol and ![[n; nu]](/images/equations/Stieltjes-WigertPolynomial/Inline16.svg)
is a q-binomial
coefficient.
Stieltjes-Wigert Polynomial
See also
q-Binomial CoefficientExplore with Wolfram|Alpha
References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 33, 1975.Referenced on Wolfram|Alpha
Stieltjes-Wigert PolynomialCite this as:
Weisstein, Eric W. "Stieltjes-Wigert Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Stieltjes-WigertPolynomial.html