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References
[A-R] K. Alladi, M. Robinson, On certain irrational values of the logarithm, Lecture Notes in Math. 751, 1–9.
[A] R. Apéry, Irrationalité de ζ(2) et ζ(3) “Journées arithmétiques de Luminy”, Astérisque no 61, 1979, 11–13.
[Ba1] A. Baker, Rational approximations to \(^3 \surd 2\) and other algebraic numbers, Quart. J. Math. Oxford, 15(1964), 375–383.
[Ba2] A. Baker, Transcendental Number Theory (Cambridge, 1975).
[Be1] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc., 11(1979), 268–272.
[Be2] F. Beukers, Legendre polynomials in irrationality proofs, Bull. Australian Math. Soc. (to appear).
[Be3] F. Beukers, The generalised Ramanujan-Nagell equation, Thesis, University of Leiden (1979), also to appear in Acta Arithmetica.
[C1] G.V. Chudnovsky, C.R. Acad. Sc. Paris, 288(1979), 607–609, 965–967, 1001–1003.
[C2] G.V. Chudnovsky, Padé-approximations to the generalized hypergeometric functions I, J. Math. pures et appl. 58(1979), 445–476.
[C3] G.V. Chudnovsky, Rational and Padé-approximations to solutions of linear differential equations and the monodromy theory, Lecture Notes in Physics 126, 136–169.
[C4] G.V. Chudnovsky, Padé-approximation and the Riemann monodromy problem, Proceedings of the NATO Advanced Study Institute, held at Cargèse, Corsica, France, June 24–July 7, 1979.
[D] Y. DOMAR, On the diophantine equation |Axn−Byn|=1, n≥5, Math. Scand. 2(1954), 29–32.
[H] Ch. Hermite, Sur la fonction exponentielle, Oeuvres III, 150–181.
[J] H. Jager, A multidimensional generalization of the Padé table, Thesis, University of Amsterdam (1964).
[L] F. Lindemann, Ueber die Zahl π, Math. Ann. 20(1882), 213–225.
[M] K. Mahler, Application of some formulae by Hermite to the approximation of exponentials and logarithms, Math. Ann. 168(1976), 200–227.
[P] A.J. van der Poorten, A proof that Euler missed… Apéry's proof of the irrationality of ζ(3), Math. Intelligencer, 1(1978), 195–203.
[R] E. Reyssat, Irrationalité de ζ(3) selon Apéry, Sém. Delange-Pisot-Poitou, 20e année, 1978/79, no 6.
[Si1] C.L. Siegel, Transcendental Numbers (Princeton 1949).
[Si2] C.L. Siegel, Die Gleichung axn−byn=c, Math. Ann. 114(1937), 57–68.
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Reukers, F. (1981). Pade-approximations in number theory. In: de Bruin, M.G., van Rossum, H. (eds) Padé Approximation and its Applications Amsterdam 1980. Lecture Notes in Mathematics, vol 888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095578
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DOI: https://doi.org/10.1007/BFb0095578
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