Abstract
Using basic number and the analogues of differentiation and integration, a q-analogue of Hermite's equation is introduced. Series solutions are given, and it is shown that polynomial forms of these solutions are orthogonal with respect to basic integration. By reversing the series representation of these solutions, a basic analogue of the Hermite polynomial is obtained for which a generating function and a three-term recurrence relation are deduced. Finally, an orthogonality relation is given.
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