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\(q\)-Macdonald function as a variation diminishing \(\ast_q\)-kernel. (English) Zbl 1524.33074

Summary: In this paper, we study the variation diminishing kernel within the context of \(q\)-calculus. We introduce the \(q\)-Macdonald function which play a central role in this study.

MSC:

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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