其中的完全规格化的勒让德函数利用gsl科学计算库（安装方法见另一篇博文）计算：

#include<gslgsl_sf_legendre.h>

double Pnm;

double sin_lat=sin(lat);//余纬cos

if(m==0)mm=1;

else mm=0;

Pnm=sqrt((2-mm)*4*pi)*pow(-1.0,m)*gsl_sf_legendre_sphPlm(n,m,sin_lat);

参考文献：

[19]. Wahr, J., M. Molenaar and F. Bryan, Timevariability of the Earth's gravity field: Hydrological and oceanic effects andtheir possible detection using GRACE. Journal of Geophysical Research: SolidEarth (1978–2012),1998. 103(B12): p. 30205-30229.

[22].Kusche,J., and E. J. O. Schrama (2005), Surface mass redistribution inversion fromglobal GPS deformation and Gravity Recovery and Climate Experiment(GRACE) gravity

data, J. Geophys. Res., 110, B09409,doi:10.1029/2004JB003556.

[23].FarrellW. E. (1972), Deformation of the Earth by surface loads. Rev. Geophys., 10, 761–797.

[24].李飞, 完全规格化缔合勒让德函数算法研究. 科技风, 2012(19).