Tight bounds for the generalized Marcum \(Q\)-function (Q837135)
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scientific article; zbMATH DE number 5602712
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tight bounds for the generalized Marcum \(Q\)-function |
scientific article; zbMATH DE number 5602712 |
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Tight bounds for the generalized Marcum \(Q\)-function (English)
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10 September 2009
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The generalized Marcum \(Q\)-function of real order is studied in this paper. The author's aim is to improve and extend some recent results of Wang to the generalized Marcum \(Q\)-function in order to deduce some sharp lower and upper bounds. The best possible upper bound is given for both cases. The key tools in the proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind. These monotonicity properties are deduced from some results on modified Bessel functions, which have been used in wave mechanics and finite elasticity.
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Marcum \(Q\)-function
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generalized Marcum \(Q\)-function
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modified Bessel functions
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lower and upper bounds
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complementary error function
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sharp bounds
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