Incomplete Bessel Functions. I

Jones, D. S.

doi:10.1017/s0013091505000490

Cited by 26 publications

(15 citation statements)

References 8 publications

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“…This integral can be solved in terms of incomplete Bessel functions [42][43][44], which can be studied in various asymptotic regimes. In particular,…”

Section: Jhep09(2020)021mentioning

confidence: 99%

Notes on lattice observables for parton distributions: nongauge theories

Debbio

Giani

Monahan

2020

J. High Energ. Phys.

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We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a framework that would allow to include the available lattice QCD data in a global analysis to extract PDFs.

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“…This integral can be solved in terms of incomplete Bessel functions [42][43][44], which can be studied in various asymptotic regimes. In particular,…”

Section: Jhep09(2020)021mentioning

confidence: 99%

Notes on lattice observables for parton distributions: nongauge theories

Debbio

Giani

Monahan

2020

J. High Energ. Phys.

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“…For this, we only present the proof of θ 1 > 0, θ 2 = 0 since another case follows by the similar arguments. Using (17) and 18, we have lim…”

Section: Proofsmentioning

confidence: 99%

Tail dependence for two skew slash distributions

Ling

Peng

2015

Statistics and Its Interface

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“…is the incomplete modified Bessel function of second kind of order ν (see [22]- [23]). The result in (8) includes many combinations of combining schemes on the first and second hops as limiting cases.…”

Section: Cdf Of End-to-end Snrmentioning

confidence: 99%

Comparison of Low-Complexity Diversity Schemes for Dual-Hop AF Relaying Systems

Gaaloul

Radaydeh

Alouini

2012

IEEE Trans. Veh. Technol.

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Abstract-This correspondence investigates the performance of two low-complexity combining schemes, which are based on one-phase or two-phase observation, to mitigate multipath fading in dual-hop amplify-and-forward (AF) relaying systems. For the one-phase based combining, a single-antenna station is assumed to relay information from multiple-antenna transmitter to multiple-antenna receiver, and the activation of the receive antennas is performed adaptively based on the second hop statistics, regardless of the first hop conditions. On the other hand, the two-phase based combining suggests using multiple single-antenna stations between the multiple-antenna transmitter and the single-antenna receiver, where the suitable set of active relays is identified according to the pre-combining end-to-end fading conditions. To facilitate comparisons between the two schemes, formulations for the statistics of the combined signal-tonoise ratio (SNR) and some performance measures are presented. Numerical and simulation results are shown to clarify the tradeoff between the achieved diversity-array gain, the processing complexity, and the power consumption.

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Incomplete Bessel Functions. I

Abstract: Incomplete Bessel functions of general order are defined. Their recurrence relations, integral representations and asymptotics are derived.

Cited by 26 publications

References 8 publications

Notes on lattice observables for parton distributions: nongauge theories

Notes on lattice observables for parton distributions: nongauge theories

Tail dependence for two skew slash distributions

Comparison of Low-Complexity Diversity Schemes for Dual-Hop AF Relaying Systems

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