The convergence problem of certain multiple Mellin-Barnes contour integrals representing H-functions in several variables

Hải, Nguyễn Thanh; Srivástava, H. M.

doi:10.1016/0898-1221(95)00003-h

Cited by 15 publications

(16 citation statements)

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“…These results were obtained through the sum of residues of several Fox H-functions with two and three variables. Here, we present the PDF and CDF in terms of the multivariable Fox H-function 5 defined in [34]…”

Section: Appendix a Results In Terms Of The Multivariate Fox H-functionmentioning

confidence: 99%

Ratio of Two Envelopes Taken From $\alpha$ -$\mu$ , $\eta$ -$\mu$ , and $\kappa$ -$\mu$ Variates and Some Practical Applications

et al. 2019

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In this paper, new, exact expressions for the probability density functions and the cumulative distribution functions of the ratio of random envelopes involving the α-µ, η-µ, and κ-µ fading distributions are derived. The expressions are obtained in terms of easily computable infinite series and also in terms of the multivariable Fox H-function. Some special cases of these ratios, namely, Hoyt/Hoyt, η-µ/Nakagami-m, κ-µ/Nakagami-m, κ-µ/η-µ with an integer µ for the η-µ variate, η-µ/η-µ with an integer µ for only one of the η-µ, and their reciprocals are found in novel exact closed-form expressions. In addition, simple closed-form expressions for the asymptotes of the probability density functions and cumulative distribution functions of all ratios, both for the lower and upper tails of the distributions are derived. In the same way, asymptotes for the bit error rate on a binary signaling channel are obtained in closed-form expressions. To demonstrate the practical utility of these new formulations, an application example is provided. In particular, the secrecy capacity of a Gaussian wire-tap channel used for device-to-device and vehicle-to-vehicle communications is characterized using data obtained from field measurements conducted at 5.8 GHz.

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Section: Appendix a Results In Terms Of The Multivariate Fox H-functionmentioning

confidence: 99%

Ratio of Two Envelopes Taken From $\alpha$ -$\mu$ , $\eta$ -$\mu$ , and $\kappa$ -$\mu$ Variates and Some Practical Applications

et al. 2019

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“…where [13] only in the replacement of x −s by x s . We have made this replacement for convenience in our applications.…”

Section: Discussionmentioning

confidence: 99%

“…Ref. [13] and references therein. (See also the recent book [14], which however deals mostly with the single variable case.)…”

Section: Introductionmentioning

confidence: 99%

“…1,1,1 (v12 , v13 , v23 ; ǫ) = − π 4v 12 v 13 v 23 v 12 + v 13 + v 23 ǫ + v 12 − v 13 − v 23 ln v 12 + v 13 − v 12 − v 23 ln v 13 + v 23 − v 12 − v 13 ln v 23 + O(ǫ) ,(C46)I 2,1,1 (v 12 , v 13 , v 23 ; ǫ) = − + 2v 12 v 23 + 2v 13 v 23 − 2v 12 v 13 v 23 − v 2 23 ǫ + v 2 12 − 2v 12 v 13 + v 2 13 + 4v 12 v 23 + 4v 13 v 23 − 6v 12 v 13 v 23 − v 2 23 + v 2 12 − v 2 13 − 2v 12 v 23 − 2v 13 v 23 + 2v 12 v 13 v 23 + v 2 23 ln v 12 + v 2 13 − v 2 12 − 2v 13 v 23 − 2v 12 v 23 + 2v 12 v 13 v 23 + v 2 23 ln v 13 − v 2 12 + v 2 13 − 2v 12 v 23 − 2v 13 v 23 + 2v 12 v 13 v 23 + v 2 23 ln v 23 + O(ǫ) , (C47)…”

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Angular integrals in d dimensions

Somogyi¹

2011

Journal of Mathematical Physics

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We discuss the evaluation of certain d dimensional angular integrals which arise in perturbative field theory calculations. We find that the angular integral with n denominators can be computed in terms of a certain special function, the so-called H-function of several variables. We also present several illustrative examples of the general result and briefly consider some applications.Comment: 30 pages, discussion slightly extended by mentioning the existence of contiguous relations for H-functions, new references adde

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“…The calculation of (14) converges rapidly, with just a few terms of the summation in most cases. In addition, an alternative expression for the approximate LCR for composite κ-µ fading was obtained, given in terms of the multivariate Fox H-function, which guarantees the convergence of the integral form [26]. This is expressed as in which L S is the appropriate contour on the complex plane S, with S = [S 1 , S 2 , S 3 ], and…”

Section: Channelmentioning

confidence: 99%

Second Order Statistics For Composite κ-μ Fading Model

Pedriali¹,

Leonardo²,

Yacoub³

2020

Anais De XXXVIII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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This paper considers second order statistics for the composite κ-µ fading model. More specifically, level crossing rate and average fade duration are calculated, and two formulations are offered: exact and approximate. The exact formulation is given in integral form, and the approximate one is written in terms of the Fox H-function, and also expressed as an infinite summation. The computation of the approximate level crossing rate and average fade duration converges quickly and are practically coincident with the exact solutions for the composite multipath-shadowing environment considered here. Additionally, as an application example, the cascaded fading channel is analyzed.

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The convergence problem of certain multiple Mellin-Barnes contour integrals representing H-functions in several variables

Cited by 15 publications

References 3 publications

Ratio of Two Envelopes Taken From $\alpha$ -$\mu$ , $\eta$ -$\mu$ , and $\kappa$ -$\mu$ Variates and Some Practical Applications

Ratio of Two Envelopes Taken From $\alpha$ -$\mu$ , $\eta$ -$\mu$ , and $\kappa$ -$\mu$ Variates and Some Practical Applications

Angular integrals in d dimensions

Second Order Statistics For Composite κ-μ Fading Model

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