论文标题
关于真实论点的二项式系数
On Binomial coefficients of real arguments
论文作者
论文摘要
众所周知，{\ mathbb r} $ in {\ mathbb r} $的实际数字$ x \的经典概念的概括是Euler的伽马函数$γ（1+x）$的值。在这方面，二项式系数的概念自然出现在真实论点的可接受价值中。 通过基本方式，事实证明，二项式系数的许多属性$ \ binom {r}α$的真实参数$ r，\，α\ in {\ mathbb r} $，例如单模式的类似物，对称性，对称性，帕斯卡尔（Pascal）的triangle，triangle，for Plassical binomial cofferications。建立了这种特殊形式的普遍二项式系数的渐近行为。
As is well-known, a generalization of the classical concept of the factorial $n!$ for a real number $x\in {\mathbb R}$ is the value of Euler's gamma function $Γ(1+x)$. In this connection, the notion of a binomial coefficient naturally arose for admissible values of the real arguments. By elementary means, it is proved a number of properties of binomial coefficients $\binom{r}α$ of real arguments $r,\,α\in {\mathbb R}$ such as analogs of unimodality, symmetry, Pascal's triangle, etc. for classical binomial coefficients. The asymptotic behavior of such generalized binomial coefficients of a special form is established.
