Bounds for the generalized Marcum Q-function
Bounds for the generalized Marcum Q-function
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DOI：
10.1016/j.amc.2010.07.024
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
Á. Baricz;Yin Sun
中科院分区：
文献类型：
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作者：
Á. Baricz;Yin Sun
本文考虑了定义为的广义Marcum Q-函数，其阶为ν>0真实的，其中a>0，B ≥ 0，Iν表示第一类修正Bessel函数。我们的目的是将一阶Marcum Q-函数的一些结果推广到广义Marcum Q-函数，从而得到一些新的上下界.此外，我们证明了所提出的界限是非常紧张的广义Marcum Q-函数的整数阶，我们推出了一些新的不等式的更一般的情况下，真实的秩序。在我们的证明中的主要工具是某些函数的单调性性质，涉及修改的第一类贝塞尔函数，这是基于两个麦克劳林级数的商的单调性的标准。
In this paper we consider the generalized Marcum Q-function of order ν>0 real, defined bywhere a>0, b⩾0 and Iνstands for the modified Bessel function of the first kind. Our aim is to extend some results on the (first order) Marcum Q-function to the generalized Marcum Q-function in order to deduce some new lower and upper bounds. Moreover, we show that the proposed bounds are very tight for the generalized Marcum Q-function of integer order, and we deduce some new inequalities for the more general case of real order. The chief tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind, which are based on a criterion for the monotonicity of the quotient of two Maclaurin series.