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arXiv · 1407.3578

Hankel determinants of the Cantor sequence

Zhi-xiong Wen·Wen Wu
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Abstract

In the paper, we give the recurrent equations of the Hankel determinants of the Cantor sequence, and show that the Hankel determinants as a double sequence is 3-automatic. With the help of the Hankel determinants, we prove that the irrationality exponent of the Cantor number, i.e. the transcendental number with Cantor sequence as its b-ary expansion, equals 2.

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Zhi-xiong Wen, Wen Wu. 2014-07-14. Hankel determinants of the Cantor sequence. https://doi.org/10.1360/012014-53

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