Formula:KLS:14.29:13

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h ~ n ⁡ ( x ; q ) - ( 1 + x 2 ) ⁢ h ~ n ⁡ ( q ⁢ x ; q ) = - q n ⁢ x ⁢ h ~ n + 1 ⁡ ( x ; q ) discrete-q-Hermite-polynomial-II-h-tilde 𝑛 𝑥 𝑞 1 superscript 𝑥 2 discrete-q-Hermite-polynomial-II-h-tilde 𝑛 𝑞 𝑥 𝑞 superscript 𝑞 𝑛 𝑥 discrete-q-Hermite-polynomial-II-h-tilde 𝑛 1 𝑥 𝑞 {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right)-(1+x% ^{2})\tilde{h}_{n}\!\left(qx;q\right)=-q^{n}x\tilde{h}_{n+1}\!\left(x;q\right)% }}}

Proof

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Symbols List

h ~ n subscript ~ ℎ 𝑛 {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}  : discrete q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII

Bibliography

Equation in Section 14.29 of KLS.

URL links

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