关于牛顿引力场的一个重要积分的解析表达式

ON AN EXACT ANALYTICAL EXPRESSION OF THE IMPORTANT INTEGRAL OF THE NEWTONIAN GRAVITATIONAL FIELD

本文将计算有限长椭圆柱体径向牛顿引力场的积分表达式中一个重要积分分解为八个反常积分,这八个积分可借助于三类椭圆函数一一积出。

In this paper an important integral in the inlegral expression for calculating the Newtonian gravitational field of the finite elliptical cyinder was resolved into eight improper integrals. By use of three kinds of elliptical function the eight integrals were integraled all, therefore, an exact expression of important integral has been obtained.