Abstract
In this paper, we obtain a result which implies, in particular, that for a quaternion z ∉ {−1, 1} with |z| = 1, the sum range of the series \( {\displaystyle \sum_n\frac{z^n}{n}} \) is a closed proper subfield of the division ring of quaternions ℍ isometrically isomorphic to the field of complex numbers ℂ.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 94, Proceedings of the International Conference “Lie Groups, Differential Equations, and Geometry,” June 10–22, 2013, Batumi, Georgia, Part 1, 2014.
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Chelidze, G., Giorgobiani, G. & Tarieladze, V. Sum Range of a Quaternion Series. J Math Sci 216, 519–521 (2016). https://doi.org/10.1007/s10958-016-2908-9
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DOI: https://doi.org/10.1007/s10958-016-2908-9