论文标题
使用量子二项式定理对二项式分布的完善
A refinement of the binomial distribution using the quantum binomial theorem
论文作者
论文摘要
$ Q $ - 特殊功能的动力学，包括超几何功能，在数学中起着核心作用，并且在物理中具有许多应用。在概率理论中，多年来引入了各种概率分布的$ q $ - analogs，包括二项式分布。在这里，我提出了通过量子二项式定理（也称为非共同$ q $ $ binmial定理）的二项式分布的新改进，其中$ q $是正式的变量，其中与基础二线实验中的成功和失败的顺序相关的信息是其代数中的。
$q$-analogs of special functions, including hypergeometric functions, play a central role in mathematics and have numerous applications in physics. In the theory of probability, $q$-analogs of various probability distributions have been introduced over the years, including the binomial distribution. Here, I propose a new refinement of the binomial distribution by way of the quantum binomial theorem (also known as the the noncommutative $q$-binomial theorem), where the $q$ is a formal variable in which information related to the sequence of successes and failures in the underlying binomial experiment is encoded in its exponent.
