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In a similar manner as in the papers [7] and [8], where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with(More)
We construct the sequence of orthogonal polynomials with respect to an inner product defined in the sense of q-integration over several intervals in the complex plane. For such introduced polynomials we prove that all zeros lie in the smallest convex hull over the intervals in the complex plane. The results are stated precisely in some special cases, as(More)
We construct q-Taylor formula for the functions of several variables and develop some new methods for solving equations and systems of equations. They are much easier for application than the well-known ones. We introduce some values for measuring their accuracy, such as (r; q)-order of convergence. We made some analogue of known methods, such as q-Newton(More)
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