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