Formula:KLS:14.08:20

<< Formula:KLS:14.08:18

formula in Al-Salam-Chihara

Formula:KLS:14.08:21 >>

${\displaystyle{\displaystyle{\displaystyle\delta_{q}Q_{n}\!\left(x;a,b\,|\,q\right){}=-q^{-\frac{1}{2}n}(1-q^{n})({\mathrm{e}^{\mathrm{i}\theta}}-{\mathrm{e}^{-\mathrm{i}\theta}})Q_{n-1}(x;aq^{\frac{1}{2}},bq^{\frac{1}{2}}|q)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle x=\cos\theta}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : Al-Salam-Chihara polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamChihara
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2

Bibliography

Equation in Section 14.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.08:18

formula in Al-Salam-Chihara

Formula:KLS:14.08:21 >>