论文标题
holtsmark函数以超几何$ _2f_2 $和airy $ \ mathrm {bi} $ functions的表达
Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions
论文作者
论文摘要
HOLTSMARK分布在等离子体物理学中有应用，用于涉及光谱线形状的电 - 微田分布，以及用于引力物体分布的天体物理学。它是稳定分布的少数示例之一，该概率密度函数的闭合形式表达已知。但是，后者在基本功能方面不可表达。在目前的工作中，我们提到的是，HOLTSMARK概率密度函数可以用超几何函数$ _2F_2 $以及第二种$ \ Mathrm {BI} $及其派生型表示。新公式比涉及$ _2F_3 $和$ _3F_4 $超测定功能的Lee提出的公式要简单。
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.
