Pith. sign in

REVIEW 1 cited by

Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2001.11893 v3 pith:SKZD4JZ2 submitted 2020-01-30 math-ph astro-ph.GAcs.GLmath.MPphysics.atom-ph

classification math-phastro-ph.GAcs.GLmath.MPphysics.atom-ph
keywords functiondistributionfunctionsholtsmarkhypergeometrictermsairydensity
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the few examples of a stable distribution for which a closed-form expression of the probability density function is known. However, the latter is not expressible in terms of elementary functions. In the present work, we mention that the Holtsmark probability density function can be expressed in terms of hypergeometric function $_2F_2$ and of Airy function of the second kind $\mathrm{Bi}$ and its derivative. The new formula is simpler than the one proposed by Lee involving $_2F_3$ and $_3F_4$ hypergeometric functions.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On an empirical method to build near-equilibrium axisymmetric and triaxial galaxy models

    astro-ph.GA 2026-07 conditional novelty 5.0 of 10

    An improved adiabatic-squeezing method with an Ornstein-Uhlenbeck noise term lets modelers prescribe the final axial ratios of near-equilibrium triaxial N-body galaxy models.

Pith tools