ABSTRACT The Laplace transforms of the transition probability density and distribution functions of the Feller process contain products of a Kummer and a Tricomi confluent hypergeometric function. The intricacies caused by the singularity at 0 of the Feller process imply that ultimately seven new inverse Laplace transforms can be derived of which four contain the Marcum Q function. The results of this paper together with a scarcely used link between the Marcum and Nuttall Q functions also provide two alternative proofs for an existing identity involving two Marcum Q functions with reversed arguments. The paper also expands the existing expression for the Marcum Q function with identical arguments and order 1. In particular, the new formula applies to all integer and fractional values of the order and is expressed in terms of the generalized hypergeometric function.

中文翻译：

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一些包含 Marcum Q 函数和 Marcum Q 函数扩展属性的拉普拉斯逆变换

摘要 Feller 过程的转移概率密度和分布函数的拉普拉斯变换包含 Kummer 和 Tricomi 汇合超几何函数的乘积。费勒过程的 0 处奇点造成的复杂性意味着最终可以导出七个新的拉普拉斯逆变换，其中四个包含 Marcum Q 函数。本文的结果以及 Marcum 和 Nuttall Q 函数之间很少使用的链接也为涉及两个具有反向参数的 Marcum Q 函数的现有恒等式提供了两种替代证明。该论文还扩展了具有相同参数和阶数 1 的 Marcum Q 函数的现有表达式。特别是，