On the H-Function With Applications

Mathai, A. M.; Saxena, R. K.; Haubold, Hans J.

doi:10.1007/978-1-4419-0916-9_1

Cited by 354 publications

(741 citation statements)

References 31 publications

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“…It has many general properties that allow one to manipulate expressions to equivalent forms, reduce the order for certain values of the parameters, etc. For details on its many useful properties, we refer the interested reader to Mathai (1978), Kilbas & Saigo (2004), or Mathai et al (2009 and the references therein.…”

Section: Spatial Propertiesmentioning

confidence: 99%

Analytical properties of Einasto dark matter haloes

Retana-Montenegro

Hese

Gentile

et al. 2012

A&A

111

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Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the Sérsic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.

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Section: Spatial Propertiesmentioning

confidence: 99%

Analytical properties of Einasto dark matter haloes

Retana-Montenegro

Hese

Gentile

et al. 2012

A&A

111

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“…The Fox H function (Fox 1961) is a generalization of Meijer G function and is also defined as an inverse Mellin transform, Kilbas & Saigo 2004;Mathai et al 2009). …”

Section: Appendix A: the Meijer G And Fox H Functionsmentioning

confidence: 99%

Analytical expressions for the deprojected Sérsic model

Baes

Gentile

2010

A&A

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The Sérsic model has become the standard for parametrizing the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sérsic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sérsic index. We use Mellin integral transforms to derive an analytical expressions for the luminosity density in terms of the Fox H function for all values of the Sérsic index. We derive simplified expressions for the luminosity density, cumulative luminosity, and gravitational potential in terms of the Meijer G function for all rational values of the Sérsic index, and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are currently available both in symbolic computer algebra packages and as high-performance computing code, our results open up the possibility to calculate the density of the Sérsic models to arbitrary precision.

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“…where an empty product is always interpreted as unity, {m, n, p, q} For other existence conditions see Mathai et al [26]. The asymptotic expansion for |z| → ∞ is obtained by integration around the poles of Γ (1 − a i − A i s) with i = 1, .…”

Section: Appendix Amentioning

confidence: 99%

Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes

Pagnini

Mura

Mainardi

2013

Phil. Trans. R. Soc. A.

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Two-particle dispersion is investigated in the context of anomalous diffusion. Two different modelling approaches related to time subordination are considered and unified in the framework of selfsimilar stochastic processes. By assuming a singleparticle fractional Brownian motion and that the two-particle correlation function decreases in time with a power law, the particle relative separation density is computed for the cases with time subordination directed by a unilateral M-Wright density and by an extremal Lévy stable density. Looking for advisable mathematical properties (for instance, the stationarity of the increments), the corresponding selfsimilar stochastic processes are represented in terms of fractional Brownian motions with stochastic variance, whose profile is modelled by using the M-Wright density or the Lévy stable density.

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On the H-Function With Applications

Cited by 354 publications

References 31 publications

Analytical properties of Einasto dark matter haloes

Analytical properties of Einasto dark matter haloes

Analytical expressions for the deprojected Sérsic model

Two-particle anomalous diffusion: probability density functions and self-similar stochastic processes

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