论文标题
通过Mellin-Barnes类型轮廓整合的精确弯曲表面积和一张薄骨的体积的分析表达
Analytical expression for the exact curved surface area and volume of a hyperboloid of one sheet via Mellin-Barnes type contour integration
论文作者
论文摘要
在本文中，我们旨在以Srivastava-daoustava-daoust三重高几何函数来获取一张肉体的精确弯曲表面积的分析表达（{\ bf先前未找到并记录在文献中}）。该派生基于通用超几何功能的Mellin-Barnes类型轮廓积分表示$ 〜_pf_q（z）$，Meijer的$ G $ - 功能，Meijer的$ G $ - 功能和系列重排技术的分解公式。此外，我们还获得了一张薄片的倍曲底体积的公式。还使用{\ it Mathematica program}来验证一个精确的弯曲表面积的封闭形式和一张纸的倍曲底体积。
In this article, we aim at obtaining the analytical expression ({\bf not previously found and recorded in the literature}) for the exact curved surface area of a hyperboloid of one sheet in terms of Srivastava-Daoust triple hypergeometric function. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function$~_pF_q(z)$, Meijer's $G$-function, decomposition formula for Meijer's $G$-function and series rearrangement technique. Further, we also obtain the formula for the volume of a hyperboloid of one sheet. The closed forms for the exact curved surface area and volume of the hyperboloid of one sheet are also verified numerically by using {\it Mathematica Program}.
