Algebraic Relations between the Hypergeometric E-Function and Its Derivatives

In this paper, we consider the generalized hypergeometric function
$$ \sum _{n=0}^\infty \frac 1{(\lambda _1+1)_n\dotsb(\lambda _t+1)_n} \biggl (\frac zt\biggr )^{tn}, \qquad\lambda _1,\dots,\lambda _t\in\mathbb Q\setminus\{-1,-2,\dots\}, $$
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.