Abstract

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 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.

中文翻译：

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使用量子二项式定理对二项式分布进行改进

摘要

q - 特殊函数的模拟，包括超几何函数，在数学中起着核心作用，在物理学中有许多应用。在概率论中，多年来引入了各种概率分布的q类比，包括二项分布。在这里，我建议通过量子二项式定理（也称为非交换q -二项式定理）对二项式分布进行新的改进，其中q是一个形式变量，其中与成功和失败序列相关的信息基础二项式实验以其指数编码。