Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Morales-Jiménez, David; López‐Martínez, F. Javier; Martos-Naya, Eduardo; Paris, José F.; Lozano, Angel

doi:10.1109/tit.2013.2291198

Cited by 26 publications

(30 citation statements)

References 38 publications

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“…The next lemma extends previously reported results on the relation between the Marcum Q function and hypergeometric function Φ 3 (b, g, t, v) (valid only for g ∈ Z + ) [16]- [17] to the case of g ∈ (0, ∞).…”

Section: Evaluation Of Laplace Transformsupporting

confidence: 86%

“…It is seen that for integer values of M, (17) with the help of (13) reduces to (14) derived in [16].…”

Section: Evaluation Of Laplace Transformmentioning

confidence: 90%

“…This function has many interesting features, see, for instance, [4]- [8], [16]- [17]. In this work, we employ a differentiation formula w.r.t.…”

Section: Marcum Q Functionmentioning

confidence: 99%

“…is the modified Bessel function of the first kind and order ν [18], Q M (α, β) is the generalized Marcum Q function [4]- [8], [16]- [17] µ 1 , µ 2 , c∈ (−∞, ∞), p ∈ (0, ∞), and α, β are either real or purely imaginary [8].…”

Section: Introductionmentioning

confidence: 99%

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Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Ermolova

Tirkkonen

2014

IEEE Trans. Signal Process.

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The evaluation of integral transforms of special functions is required in different research and practical areas. Analyzing the κ-µ fading distribution also khown as the generalized Rician distribution, we find out that the assessment of a few different performance metrics, such as the probability of energy detection of unknown signals and outage probability under co-channel interference, involves the evaluation of an infinite-range integral, which has the form of Laplace transform of product of Marcum Q, Bessel I, and power functions. We evaluate this integral in a closed-form and present numerical estimates. Index TermsBessel I function, co-channel interference, confluent hypergeometric functions of two variables, detection probability, generalized fading distributions, Laplace transform, Marcum Q function, outage probability.

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Section: Evaluation Of Laplace Transformsupporting

confidence: 86%

“…It is seen that for integer values of M, (17) with the help of (13) reduces to (14) derived in [16].…”

Section: Evaluation Of Laplace Transformmentioning

confidence: 90%

“…This function has many interesting features, see, for instance, [4]- [8], [16]- [17]. In this work, we employ a differentiation formula w.r.t.…”

Section: Marcum Q Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Ermolova

Tirkkonen

2014

IEEE Trans. Signal Process.

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“…In Fig. 1, we represent ε 1 (α, x) for different values of α, considering the approximations introduced in (3) and (6). When the Gaussian Q-function approximation is used, for small values of α, we observe how a relatively large value of x ≈ 3.5 is required to obtain an error in the range of 1%.…”

Section: Approximation Errormentioning

confidence: 99%

Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum <inline-formula> <tex-math notation="TeX">$Q$</tex-math></inline-formula>-Functions

López‐Martínez

Romero-Jerez

2015

IEEE Trans. Veh. Technol.

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Abstract-In this paper, we derive two simple and asymptotically exact approximations for the function defined as ∆Qm(a, b) Qm(a, b) − Qm(b, a). The generalized Marcum Qfunction Qm(a, b) appears in many scenarios in communications in this particular form, referred to as symmetric difference of generalized Marcum Q-functions or difference of generalized Marcum Q-functions with reversed arguments. We show that the symmetric difference of Marcum Q-functions can be expressed in terms of a single Gaussian Q-function for large and even moderate values of the arguments a and b. A second approximation for ∆Qm(a, b) is also given in terms of the exponential function. We illustrate the applicability of these new approximations in different scenarios:

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On New Formulas for the Cumulative Distribution Function of the Noncentral Chi-Square Distribution

Maširević

2017

Mediterr. J. Math.

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The main aim of this article is to derive three new formulas for the cumulative distribution function of the noncentral chi-square distribution. The main advantage of such formulas is that they are given in terms of modified Bessel functions, leaky aquifer function and generalized incomplete gamma function which have a wide range of applications. In addition, the computational efficiency of the newly derived formulas versus already known formulas is established.Mathematics Subject Classification. Primary 62E99, 33C10; Secondary 65B10, 33E20.

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Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Cited by 26 publications

References 38 publications

Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum <inline-formula> <tex-math notation="TeX">$Q$</tex-math></inline-formula>-Functions

On New Formulas for the Cumulative Distribution Function of the Noncentral Chi-Square Distribution

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