Application of singular elliptic functions to the search for some properties of Legendre polynomials

Abstract

In this work the following theorem is proven. Let it be a negative integer rational number without squares. Consider a square field k (Nm) and let it be the basis of some ideal of this field. Moreover, let p (u, ω1, ω2) be the famous Weierstrasse definition (in the future we will dimerize the basis ω1, ω2 so that the ratio ω1, ω2 has a positive imaginary part), which follows the following differential equation (see article).