https://doi.org/10.1140/epjp/s13360-020-00248-4
Regular Article
Expression of the Holtsmark function in terms of hypergeometric 
and Airy Bi functions
CEA, DAM, DIF, 91297, Arpajon, France
* e-mail: jean-christophe.pain@cea.fr
Received:
27
October
2019
Accepted:
28
January
2020
Published online:
10
February
2020
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 and of Airy function of the second kind Bi and its derivative. The new formula is simpler than the one proposed by Lee involving 
and 
hypergeometric functions.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
