Aiming at the practical spherical function analysis of monthly mean hemispherical potential hight field,it was compared and analyzed that calculation errors of the modulus and cross angle of the standardized associated Legendre function P_m+2k^m using common trapeziod formula,Simpson integral formula and WU Xin-yuan′s numerical integral expression.The results are given as follow:when m=0,1,the calculation precision of the modulus and cross angle of P_m+2k^m by WU Xin-yuan′s expression is better than those by the other two common integral formula;when m≥2,the precision of trapeziod integral formula is higher than that of WU Xin-yuan′s expression,whose errors for the modulus and cross angle calculation is still below 10^-4 and 2×10^-3°,respectively.Because the variance spectrum of monthly mean hemispherical potential hight field spherical function has the basic character of reduced dimensionality and low order,using WU Xin-yuan′s expression is able obviously to improve the spherical function analysis precision of monthly mean hemispherical potential hight field.