Some Sufficient Conditions of a Given Series with Rational Terms Converging to an Irrational Number or a Transcendental Number


Affiliations

  • Shanghai Putuo University, Department of Mathematics, Shanghai, 200062, China
  • Shanghai Jiaotong University, Department of Mathematics, Shanghai, 200240, China

Abstract

In this paper, we generalize Erdors' result on irrationality of some specic fast convergent series, and give out various application examples even in dynamical system, based on it, we propose a conjecture on the irrationality of E series.

Keywords

Diophantine Approximation, Irrational Number, Transcendental Number.

Subject Discipline

Mathematical Sciences

Full Text:

References

H. Cremer, Zum Zentrumproblem, Math. Ann., 98 (1927), 151 – 163.

P. Erdos, Some problems and result on the irrationality of sum of infinite series, J. Math. Sci., 10 (1975), 1 – 7.

L. K. Hua, Introduction to number theory, Scientific Press, Beijing, 1979.

J. Sandor, Some classes of irrational numbers, Studia Univ. Babes-Bolyai-Math, 29 (1984), 3 – 12.


Refbacks

  • There are currently no refbacks.