The Journal of the Indian Mathematical Society

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


Affiliations
1 Department of Mathematics, Shanghai Putuo University, Shanghai, 200062, China
2 Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, China
     

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

Abstract Views: 228  |  PDF Views: 0

Authors

Yun Gao
Department of Mathematics, Shanghai Putuo University, Shanghai, 200062, China
Jining Gao
Department of Mathematics, Shanghai Jiaotong University, 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.