Algebraic Relations between the Hypergeometric E-Function and Its Derivatives

In this paper, we consider the generalized hypergeometric function $$\sum\limits_{n = 0}^\infty {\frac{1}{{\left( {{\lambda }_{1} + 1} \right)_n ...\left( {{\lambda }_t + 1} \right)_n }}} \left( {\frac{z}{t}} \right)^{tn} ,{ \lambda }_{1} ,...,{\lambda }_{t} \in \mathbb{Q}\backslash \left\{ { - 1, - 2,...} \right\},$$ where t is an even number, and its derivatives up to the order t- 1 inclusive. In the case of algebraic dependence between these functions over $\mathbb{C}$ (z), a complete structure of algebraic relations between them is given.