论文标题
一类Legendre公式的渐近学
Asymptotics on a class of Legendre formulas
论文作者
论文摘要
令$ f $是单个变量的实值函数，使其对素数为正。在本文中，我们构建了与$ f $相关的阶乘，$ n！_f $，称为“关联的legendre公式”或“ $ f $”，并显示，符合某些标准，即$ n！_f $满足弱的stirling近似值。作为应用程序，我们将对Bhargava阶乘对一组素数和鲜为人知的Legendre公式进行薄弱的近似值。
Let $f$ be a real-valued function of a single variable such that it is positive over the primes. In this article, we construct a factorial, $n!_f$, associated to $f$, called the associated Legendre formula, or $f$-factorial, and show, subject to certain criteria, that $n!_f$ satisfies a weak Stirling approximation. As an application, we will give weak approximations to the Bhargava factorial over the set of primes and to a less well-known Legendre formula.
