标题： 克莱布希-戈登系数，超几何函数和二项分布 显示英文标题

标题： Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution

摘要： 一个退化的Clebsch-Gordan系数的特殊情况可以用三个二项式系数来表示。 这样的公式，可以通过标准的阶梯算子过程得到，也可以从Racah-Shimpuku公式或用$_3F_2$超几何函数表示的Clebsch-Gordan系数表达式推导出来。 O'Hara通过二项式随机变量对这个Clebsch-Gordan系数的有趣解释，也可以与超几何函数（$_2F_1$）相关联，在其中一个参数趋于无穷大的情况下。 这强调了Clebsch-Gordan系数、超几何函数以及在角动量量子理论框架下尚未被充分开发的概率概念之间的联系。 显示英文摘要

摘要： A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in terms of $_3F_2$ hypergeometric functions. The O'Hara interesting interpretation of this Clebsch-Gordan coefficient by binomial random variables can also be related to hypergeometric functions ($_2F_1$), in the case where one of the parameters tends to infinity. This emphasizes the links between Clebsch-Gordan coefficients, hypergeometric functions and, what has been less exploited until now, the notion of probability within the framework of the quantum theory of angular momentum.