Geodesic
On the irrationality of the values of hypergeometric functions
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 243-257 
V. N. Sorokin. On the irrationality of the values of hypergeometric functions. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 243-257. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a14/
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     title = {On~the irrationality of the values of hypergeometric functions},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_1_a14/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper investigates the arithmetic properties of the values of certain hypergeometric functions at points in an imaginary quadratic field $\mathbf I $. Under certain conditions it is proved that these values are linearly independent over $\mathbf I $. An effective lower bound is given for a linear form, which contains the maximum modulus of its coefficients. An estimate is also given which depends on the bounds within which each of the coefficients varies. Bibliography: 11 titles.

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[5] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, t. 1, Nauka, M., 1973

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[7] Nikishin E. M., “O sisteme markovskikh funktsii”, Vestn. MGU. Ser. matem., mekhan., 1979, no. 4, 60–63 | MR | Zbl

[8] Nikishin E. M., “O sovmestnykh approksimatsiyakh Pade”, Matem. sb., 113(155) (1980), 499–519 | MR | Zbl

[9] Nikishin E. M., “Ob irratsionalnosti znachenii $F(x,s)$”, Matem. sb., 109(151) (1979), 410–417 | MR | Zbl

[10] Nikishin E. M., “Ob odnom nabore stepennykh ryadov”, Sibir. matem. zhurn., XXII:4 (1981), 164–168 | MR

[11] Baker A., “Rational approximations to $2^{3/2}$ and other algebraic numbers”, Quart. J. Math., 15:60 (1964), 375–383 | DOI | MR | Zbl