The Continued Fractions of Certain Exponentials

Pratchayaporn DOEMLIM; Vichian LAOHAKOSOL; Janyarak TONGSOMPORN

doi:10.48048/wjst.2019.6956

The Continued Fractions of Certain Exponentials

Authors

Pratchayaporn DOEMLIM School of Science, Walailak University, Nakhon Si Thammarat 80160
Vichian LAOHAKOSOL Department of Mathematics, Kasetsart University, Bangkok 10900
Janyarak TONGSOMPORN School of Science, Walailak University, Nakhon Si Thammarat 80160

DOI:

https://doi.org/10.48048/wjst.2019.6956

Keywords:

Hurwitz continued fraction, continued fraction expansion, exponential number

Abstract

In 1954, Perron constructed simple continued fractions of e1/k and e2/k where k is a positive integer. These are called Hurwitz continued fractions. Using the method given in Perron’s book, we determine explicit shapes of simple continued fractions of ke1/k; 1 k e1/k and 2e.

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References

H Cohn. A Short proof of the simple continued fraction expansion of e. Am. Math. Monthly 2006; 113, 57-62.

CS Davis. On some simple continued fractions connected with e2/k. J. London Math. Soc.. 1945; 20, 194-8.

T Komatsu. A proof of the continued fraction expansion of e2/s. Integers. 2007, A30.

O Perron. Die Lehre von den Kettenbrüchen, Band I, Teubner, Stuttgart, 1954.

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Published

2019-05-29

How to Cite

DOEMLIM, P., LAOHAKOSOL, V., & TONGSOMPORN, J. (2019). The Continued Fractions of Certain Exponentials. Walailak Journal of Science and Technology (WJST), 16(9), 615–624. https://doi.org/10.48048/wjst.2019.6956