For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function, has two entire functions C q (z) and S q (z) as linearly independent solutions. The functions C q (z) and S q (z) are orthogonal on a discrete set. We consider Fourier expansions in these functions and derive analytic bounds on the roots of S q (z).
Abstract. We present a general procedure for finding linear recurrence relations for the solutions of the second order difference equation of hypergeometric type. Applications to wave functions of certain discrete system are also given.
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to q-classical polynomials are given. 2000 Mathematics Subject Classification 33D15, 33D45 1 Γ(s − z + µ) Γ(s − z) , ν ∈ R,
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