Methods of local gravitational field presentation using nonorthogonal functions are considered. Analysis of SCHA, ASHA and TOSCHA techniques of local field modeling on spherical cap and spherical segment is accomplished according to density distribution of initial data. Approximate formula for finding eigenvalues of differential equation of associated spherical functions is found and compared with other formulas. This approach involves using of associated Legendre functions of integer degree and noninteger order. These functions form two sets of functions. They are mutually orthogonal over the spherical cap in each set. However, in general these functions are not orthogonal. Thus, for using both of these sets of functions it is traditionally used least squares method. However, for higher orders it is quite difficult to compute eigenvalues and norms of these functions. such case it is possible to project the initial data on the hemisphere and to use associated Legendre functions of integer degree and integer order. The properties of these functions are similar to properties of functions on the spherical cap. Traditionally, initial data is selected in the nodes of grid, especially for fast computations. There are many kinds of uniform grids, which allow to speed up the process of computation the unknown harmonic coefficients. Among these grids it is possible to allocate the geographical grid, Gauss grid and others. Thus, grid is developed to accommodate the initial data and is defined its basic properties in the segment of sphere and hemisphere .
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