Geodesic
On the linear independence of some functions
Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 145-151.

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We consider hypergeometric functions and functions obtained from them by the differentiation with respect to parameter. For such functions a problem of their linear independence over the field of rational fractions is solved. 
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P. L. Ivankov. On the linear independence of some functions. Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 145-151. http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a14/

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[2] Ivankov P. L., “O lineinoi nezavisimosti znachenii nekotorykh funktsii”, Fundamentalnaya i prikladnaya matematika, 1:1 (1995), 191–206 | MR | Zbl

[3] Galochkin A. I., “On effective bounds for certain linear forms”, New Advances in Transcendence theory, Cambridge–New Rochell–Melbourne–Sydney, 1988, 207–215 | MR