论文标题
通过Mellin-Barnes类型轮廓整合的半elilipsoid的精确弯曲表面积的分析表达式
Analytical expressions for the exact curved surface area of a hemiellipsoid via Mellin-Barnes type contour integration
论文作者
论文摘要
在本文中，我们旨在以根据Appell的第一类的双重高几幅功能来获取半ellpsoid的精确弯曲表面积的分析表达式（{\ bf {\ bf {\ bf}）。该派生基于通用高几何功能的Mellin-Barnes类型轮廓积分表示$ 〜_pf_q（z）$，Meijer的$ G $ - 功能和高斯功能的分析连续性公式。此外，我们获得了一些与椭圆形，pr酸球体和扁平球体有关的特殊情况。还通过使用{\ it Mathematica程序}来验证半ellpsoid的精确弯曲表面积的封闭形式。
In this article, we aim at obtaining the analytical expressions ({\bf not previously found and not recorded in the literature}) for the exact curved surface area of a hemiellpsoid in terms of Appell's double hypergeometric function of first kind. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function$~_pF_q(z)$, Meijer's $G$-function and analytic continuation formula for Gauss function. Moreover, we obtain some special cases related to ellipsoid, Prolate spheroid and Oblate spheroid. The closed forms for the exact curved surface area of a hemiellpsoid are also verified numerically by using {\it Mathematica Program}.
