本文阐明了量子化学从头计算中的Gauss积分函数Fm(z)用递推公式计算时误差传递和变化的定量规律.提出了向上和向下递推相结合进行Fm(z)系列计算的最优方案,它保证绝对误差在递推过程中只减不增,对递推基项无附加的精度要求,可用于改进各种Fm(z)程序.本法与Schaad公式相结合,用于P、d、f和g型Gauss函数的计算,可分别节约加法运算40％以上和乘法、指数运算60%以上. In this paper, the quantitative law of error transfer and change in Gauss integral function Fm (z) in ab initio calculation is described. The optimal combination of upward and downward recursion for Fm (z) series calculation is proposed It ensures that the absolute error is reduced only during the recursion process and that there is no additional accuracy requirement for the recursive base term and can be used to improve various Fm (z) procedures. This method, combined with the Schaad formula, The calculation of d, f and g Gauss functions can save more than 40% of addition and multiplication respectively and 60% of exponential operation.