Nonlinear recurrence relations for modified Q-discrete hermite orthogonal polynomials

We consider a class of polynomials (h) over tilde (n)(x; q) defined by (h) over tilde (n)(x; q) = (a(n)x + b(n))h(n-1) (x; q) + (1-a(n))h(n) (x; q), n = 0, 1, 2,..., a(0) not equal 1, where h(n) (x; q) are monic q-discrete Hermite orthogonal polynomials satisfying the following three-term recurrence relation: h(n+1) (x; q) = xh(n) (x; q) + q(n-1) (q(n-1))h(n-1) (x; q), n >= 1, h(1)(x; q) = x, h(0)(x; q) = 1. We derive explicitly the sequences a(n) and b(n), and provide the second order difference equation.