Abstract:
We consider hypergeometric functions satisfying homogeneous linear differential equations of arbitrary order. We prove general theorems on the algebraic independence of the solutions of a set of hypergeometric equations as well as of the values of these solutions at algebraic points. The conditions of most theorems are necessary and sufficient.
Keywords:generalized hypergeometric function, linear differential equation, algebraic independence of solutions, Galois group, differential field, transcendence degree, contiguous functions.
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