By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel’s exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel’s method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel’s method in any situation. The same approach is applicable to the geomagnetic field computation.

中文翻译：

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棱柱形重力场标准算法的速度和精度改进

通过利用反正切函数和对数的加法定理，我们开发了Bessel精确公式的新表达式，以使用某些解析函数的三重差来计算棱柱形重力场。由于所需的先验功能的数量大大减少，因此新表达式的使用很快。数值实验表明，在计算均匀矩形平行六面体的重力势，重力矢量和重力梯度张量时，新方法的运行速度分别比贝塞尔方法快2.3倍，2.3倍和3.7倍。此外，新方法的计算精度略有提高。因此，在任何情况下都可以使用新方法代替贝塞尔方法。相同的方法适用于地磁场计算。