Abstract:In view of the calculation accuracy and stability of the fully normalized associated Legendre functions(fnALFs) and the applicability of the commonly column-wise recurrence formulas, four types of column-wise recurrence formulas are given based on the principle formula of Legendre function. The research shows that the universality of the indirect algorithm of Belikov’s column-wise recurrence formulais only about 3 100 orders, while the universality of fully normalized direct algorithm is about 15 000 orders. The formula given by Belikov is the best among all the column-wise recurrence formulas. The smaller the coefficient in the column-wise recurrence formulas, the slower the overflow phenomenon appears, the higher the recurrence order, the better the recursive formula.