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arXiv · 2206.00935

On a continued fraction expansion of the special function and an explicit expression of the continued fraction convergents

Naoki Murabayashi·Hayato Yoshida
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Abstract

In this paper we define "a continued fraction expansion of the exponential integral $E_{1}(x)$ at infinity", which is analogous to the regular continued fraction expansion of real numbers, and prove that this expansion gives the same continued fraction. Moreover, we give concrete representations of rational functions which are obtained by truncating the continued fraction.

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Naoki Murabayashi, Hayato Yoshida. 2022-06-02. On a continued fraction expansion of the special function and an explicit expression of the continued fraction convergents. https://arxiv.org/abs/2206.00935

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