Geodesic
On simultaneous approximations of some hypergeometric functions
Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 184-191.

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In this paper we propose effective construction of simultaneous approximations for some hypergeometric functions of a special type and their derivatives with respect to parameter. This construction is made use of for the achievement of the lower estimates of numerical linear forms of the values of such functions. Some parameters of these functions can be irrational.
Keywords: hypergeometric functions, effective construction, simultaneous approximations, linear forms. 
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P. L. Ivankov. On simultaneous approximations of some hypergeometric functions. Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 184-191. http://geodesic.mathdoc.fr/item/CHEB_2024_25_1_a14/

[1] Ivankov, P. L., “On the use of joint approximations for studying the arithmetic nature of values of hypergeometric functions”, Science and Education, 12 (2012), 135–143

[2] Ivankov, P. L., “On the use of the theory of divisibility in quadratic fields for obtaining estimates of some linear forms”, Science and Education, 11 (2013), 129–138

[3] Ivankov, P. L., “On differentiation on the parameter of hypergeometric functions of the of special kind”, Izvestiya Vuzov. Mathematics, 12 (2019), 71–81 | Zbl

[4] Shidlovsky, A. B., Transcendental numbers, Nauka, M., 1987

[5] Ivankov, P. L., “On linear independence of values of some functions”, Fundamental and Applied Mathematics, 1:1 (1995), 191–206 | MR | Zbl

[6] Galochkin, A. I., “On arithmetic properties of values of some integer hypergeometric functions”, Siberian Mathematical Journal, 17:6 (1976), 1220–1235 | MR | Zbl

[7] Chudnovsky, D. W., Chudnovsky G.W., “Applications of Pade approximation to diophantine inequalities of G-functions”, Lecture Notes in Math., 1135, 1985, 9–51 | DOI | MR | Zbl

[8] Ivankov, P. L., “On linear independence of values of some hypergeometric functions over an imaginary quadratic field”, Chebyshevskii Sbornik, 20:4 (2020), 155–166 | DOI

[9] Ivankov, P. L., “Efficient construction of joint approximations for hypergeometric functions of special kind”, Algebra, number theory and discrete geometry: modern problems, applications and problems of history, Proceedings of the XVIII International Conference on the 100-th Anniversary of the Birth of Professors B. M. Bredikhin, V. I. Nechaev and S. B. Stechkin (Tula, 2020), 255–256