Fórmulas y teoremas de adición de las funciones elípticas de Jacobi

Abstract

This paper is dedicated to the systematic study of the formulae and addition theorems of the Jacobi's functions. Starting from fundamental properties, we show most known equations and, at the same time, we classify and sort them in the most useful form, in order to get a satisfactory formulary. The addition theorems are expressed in vectorial language, as five parallel vectors in four dimensions. We also discover 16 orthogonal vectors to the above mentioned direction, with a very simple structure, notwithstanding only three of them are linearly independent. We group them in sets of four vectors, also orthogonal to one different vector of the standard basis. In each group of four vectors, only two of them are linearly independent, therefore we associate an antisymmetric tensor to each quartet.