椭球体表面积、电容和退磁因子的封闭解
Closed form solution for the surface area, the capacitance and the demagnetizing factors of the ellipsoid
摘要：
我们导出了浸入欧氏空间R^3中的椭球的表面积、电容和退磁因子的封闭形式解。椭球的上述几何和物理性质的精确解用二元Appell的广义超几何函数优美地表示。导出了椭球的表面积、退磁因子和电容的精确解定理的各种极限情况，这些结果与已知的长椭球和扁椭球以及球体的解一致。简要讨论了所取得的成果在物理学、生物学和空间科学等各个科学领域的可能应用。
英文摘要：
We derive the closed form solutions for the surface area, the capacitance and the demagnetizing factors of the ellipsoid immersed in the Euclidean space R^3. The exact solutions for the above geometrical and physical properties of the ellipsoid are expressed elegantly in terms of the generalized hypergeometric functions of Appell of two variables. Various limiting cases of the theorems of the exact solution for the surface area, the demagnetizing factors and the capacitance of the ellipsoid are derived, which agree with known solutions for the prolate and oblate spheroids and the sphere. Possible applications of the results achieved, in various fields of science, such as in physics, biology and space science are briefly discussed.
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