where \(L_{i}\) is the Legendre polynomial of degree i.

When up to the term of second degree of Legendre polynomial extended to a two-dimensional plane is employed as a basic curved surface, a random curved surface having the degree of freedom of 6 is generated.

For the first example, I just want an example to show that the solution is exact for polynomials of degree 2 n − 1 {\displaystyle 2n-1} , using the n {\displaystyle n} th degree Legendre polynomial.