Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive methods for computing the C-G coefficients are often unstable for large quantum numbers due to numerical overflow or underflow. In this paper, we present an improved method, called the sign-exponent recurrence, for the recursive computation of C-G coefficients. The result shows that the proposed method can significantly improve the stability of the computation without losing its efficiency, producing accurate values for the C-G coefficients even with very large quantum numbers.

快速，准确和稳定地计算Clebsch-Gordan（CG）系数始终是可取的，例如，在光散射模拟，多极场的平移，量子物理学和化学中。由于数值上溢或下溢，当前用于计算CG系数的递归方法对于大量子数通常不稳定。在本文中，我们提出了一种改进的方法，称为符号指数递归，用于CG系数的递归计算。结果表明，所提出的方法可以显着提高计算的稳定性，而不会损失其效率，即使具有非常大的量子数，也可以产生CG系数的准确值。