Analytic Error Function and Numeric Inverse Obtained by Geometric Means

[摘要] Using geometric considerations, we provided a clear derivation of the integral representation for the error function, known as the Craig formula. We calculated the corresponding power series expansion and proved the convergence. The same geometric means finally assisted in systematically deriving useful formulas that approximated the inverse error function. Our approach could be used for applications in high-speed Monte Carlo simulations, where this function is used extensively.

[学科分类] 农艺学与作物科学

[关键词] error function;analytic function;inverse error function;approximations62E15;62E17;60E15;26D15