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ON THE TRANSCENDENCE OF SOME INFINITE SERIES

Published online by Cambridge University Press:  01 January 2008

JAROSLAV HANČL  and
JAN ŠTĚPNIČKA
JAROSLAV HANČL
Affiliation:
Department of Mathematics and Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic e-mail: hancl@osu.cz, janstepnicka@centrum.cz
JAN ŠTĚPNIČKA
Affiliation:
Department of Mathematics and Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic e-mail: hancl@osu.cz, janstepnicka@centrum.cz
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Abstract

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The paper deals with a criterion for the sum of a special series to be a transcendental number. The result does not make use of divisibility properties or any kind of equation and depends only on the random oscillation of convergence.

Keywords

11J81
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 1 , January 2008 , pp. 33 - 37
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Duverney, D., Transcendence of a fast converging series of rational numbers, Math. Proc. Camb. Phil. Soc. 130 (2) (2001), 193–207.CrossRefGoogle Scholar
2.Erdös, P., Some problems and results on the irrationality of the sum of infinite series, J. Math. Sci. 10 (1975), 1–7.Google Scholar
3.Hančl, J., Expression of real numbers with the help of infinite series, Acta Arith. LIX (2) (1991), 97–104.CrossRefGoogle Scholar
4.Hančl, J., Two criteria for transcendental sequences, Le Matematiche, LVI (1) (2001), 149–160.Google Scholar
5.Nishioka, K., Mahler functions and transcendence, Lecture Notes in Mathematics No. 1631 (Springer-Verlag, 1996).CrossRefGoogle Scholar
6.Parshin, A. N. and Shafarevich, I. R. (Eds.), Encyclopaedia of Mathematical Sciences, Volume 44, Number Theory IV (Springer-Verlag, 1998).CrossRefGoogle Scholar
7.Roth, K. F., Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20.CrossRefGoogle Scholar
8.Shidlovskii, A. B., Transcendental numbers (Walter de Gruyter, 1989).CrossRefGoogle Scholar