Abstract:
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.
Fulltext:
PDF file (250 kB)
