Difference between revisions of "Continuous q-Hermite polynomial"
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| + | The continuous $q$-Hermite polynomials are defined by | ||
| + | $$\left\{ \begin{array}{ll} | ||
| + | H_0(x|q)=1 \\ | ||
| + | H_1(x|q)=2x \\ | ||
| + | H_{n+1}(x|q) = 2xH_n(x|q) - (1-q^n)H_{n-1}(x|q). | ||
| + | \end{array} \right.$$ | ||
=References= | =References= | ||
[http://arxiv.org/pdf/1101.2875v4.pdf On the q-Hermite polynomials and their relationship with some other families of orthogonal polynomials] | [http://arxiv.org/pdf/1101.2875v4.pdf On the q-Hermite polynomials and their relationship with some other families of orthogonal polynomials] | ||
Revision as of 16:49, 20 May 2015
The continuous $q$-Hermite polynomials are defined by $$\left\{ \begin{array}{ll} H_0(x|q)=1 \\ H_1(x|q)=2x \\ H_{n+1}(x|q) = 2xH_n(x|q) - (1-q^n)H_{n-1}(x|q). \end{array} \right.$$
