论文标题
在Barnes双伽马功能上
On the Barnes double gamma function
论文作者
论文摘要
我们旨在实现以下三个目标。首先，我们收集Barnes Double Gamma函数$ G（Z;τ）$的所有已知定义，转换属性和功能身份。其次，我们得出了用于数值计算双伽马函数的算法，并将其完整的渐近扩展为$ z \ to \ infty $。第三，我们得出了一些新属性，包括新产品标识和伽马模块化表单$ c（τ）$和$ d（τ）$的新表示。
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function $G(z;τ)$. Second, we derive an algorithm for numerically computing the double gamma function and present its complete asymptotic expansion as $z\to \infty$. Third, we derive some new properties, including a new product identity and new representations of the gamma modular forms $C(τ)$ and $D(τ)$.
