Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911810904391680 |
|---|---|
| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_11893 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions Pain, Jean-Christophe Mathematical Physics Astrophysics of Galaxies General Literature Atomic Physics 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. |
| title | Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions |
| topic | Mathematical Physics Astrophysics of Galaxies General Literature Atomic Physics |
| url | https://arxiv.org/abs/2001.11893 |