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The generalized Marcum \(Q\)-function: an orthogonal polynomial approach. (English) Zbl 1229.33032

Summary: A novel power series representation of the generalized Marcum \(Q\)-function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is shown, together with a convergence speed analysis by means of truncation error. A brief review of related studies and some numerical results are also provided.

MSC:

33E20 Other functions defined by series and integrals
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