• Corpus ID: 39855061

# A CRITERION OF IRRATIONALITY

@article{Duverney1996ACO,
title={A CRITERION OF IRRATIONALITY},
author={D. Duverney},
journal={Portugaliae Mathematica},
year={1996},
volume={53},
pages={229-237}
}
• D. Duverney
• Published 1996
• Mathematics
• Portugaliae Mathematica
We generalize P. Gordan's proof of the transcendence of e ((3); (5), p. 170), and obtain a criterion of irrationality (Theorem 1 below). Using this criterion, we can prove the irrationality of f(z) = 1 + P+1 n=1 z n v1 v2¢¢¢vn qn(n+1)=2 , when z, q and vn satisfy
4 Citations
Irrationality results for values of generalized Tschakaloff series II
• Mathematics
• 2004
Abstract The study of irrationality properties of values of the generalized Tschakaloff series f(x) defined by (1.2) below was initiated by Duverney (Portugal. Math. 53(2) (1996) 229; Period. Math.
Irrationality measure of sequences
• Mathematics
• 2005
The new concept of an irrationality measure of sequences is introduced in this paper by means of the related irrational sequences. The main results are two criteria characterising lower bounds for
TSUKUBA J. MATH.Vol. 27 No. 2 (2003), 341-357
• 2004
The main result of this paper is a general criterion for linearly unrelated sequences which does not depend on divisibility. A criterion for irrational sequences is presented as a consequence.
A general criterion for linearly unrelated sequences
• Mathematics
• 2003
The main result of this paper is a general criterion for linearly unrelated sequences which does not depend on divisibility. A criterion for irrational sequences is presented as a consequence.

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