In this note, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the moments of Student's t-distribution can be written in terms of the familiar Gamma function, Kummer's confluent hypergeometric function, and the hypergeometric function.

翻译：在本说明中, 我们通过一个统一的概率框架, 得出学生在单维立体和更高维度的 t - 分布时刻的封闭形式公式。 有趣的是, 学生 t - 分布时刻的封闭形式表达式可以用熟悉的 Gamma 函数、 Kummer 的 conduleent 超几何函数和超几何函数来写。