Algebraic and linear independence of values of certain classes of entire functions (Q584311)

Let \(f(z)=\sum^{\infty}_{n=0}c_ nz^{tn}\), \(t\in {\mathbb{N}}\), \(c_ n\in {\mathbb{K}}\) (algebraic number field) be an entire function and let \(\gamma_ 0,\gamma_ 1,...,\gamma_ n,...\in K\) be the solutions of a certain recurrence sequence of order k. In this paper, the author gives a general theorem of algebraic independence of values of the function \(F(z)=\sum^{\infty}_{n=0}\gamma_ nc_ nz^{tn}\) and its derivatives at algebraic points.