Abstract:
We consider hypergeometric functions and their
derivatives (including with respect to parameter). For such
functions we prove theorems concerning their linear independence
over the field of rational fractions. In this connection we apply
method that has been specially developed for this purpose. The
proven independence of the functions under consideration is
subsequently used for the investigation of arithmetic properties of
their values by means of the modified Siegel's method.
Some papers have been previously published containing in case of
absence of differentiation with respect to parameter necessary and
sufficient conditions for the aforementioned linear independence.
For differentiated with respect to parameter functions there have
been published many theorems concerning their algebraic
independence. But by means of all these theorems one is unable to
establish linear independence of the functions which are considered
in this paper.
Keywords:hypergeometric function, linear independence, differentiation with respect to parameter.
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