1、The recurrence relations of the coefficients of the Earth's gravity have been given in this paper.

2、Complete solving of the n-chain of rings based on recurrence relations and gray code

3、The parent function is the most ideal tool to study functions defined by recurrence relations.

4、This paper gives an explicit solution to linear non-homogeneous recurrence relations with constant coefficients by means of generating function.

5、A new method of fast computing the spherical harmonic perturbation on satellites and the recurrence relations of the coefficients of the Earth's gravity are given.

6、According to the symmetry of the triangle window function and the recurrence relations of triangle filter, the practical algorithm of the approximated Gaussian filter is obtained.

7、Then a new algorithm of brivate vector -valued rational interpolants by means of complexification of the knots and backward three-term recurrence relations is given.

8、The limited condition of alternate permutation to utilize character of chessman polgnomial sets up recurrence relations and educes two math question about formula of permutation figure.