Geodesic
$q$-Hermite polynomials and $q$-oscillators
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 81-90

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New $q$-analog of Hermite polynomials was suggested. This definition was based on the notion of deformed oscillator and related with symmetric, with respect to replacement $q\leftrightarrow q^{-1}$, form of $q$-analysis. 
@article{ZNSL_1992_199_a6,
     author = {E. V. Damaskinsky and P. P. Kulish},
     title = {$q${-Hermite} polynomials and $q$-oscillators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {81--90},
     publisher = {mathdoc},
     volume = {199},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a6/}
}
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E. V. Damaskinsky; P. P. Kulish. $q$-Hermite polynomials and $q$-oscillators. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 81-90. http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a6/