Abstract
We give a formula for \(f(\eta ),\) where \(f:{\mathbb {C}} \rightarrow {\mathbb {C}}\) is a continuously differentiable function satisfying \(f(\bar{z}) = \overline{f(z)},\) and \(\eta \) is a dual quaternion. Note this formula is straightforward or well known if \(\eta \) is merely a dual number or a quaternion. If one is willing to prove the result only when f is a polynomial, then the methods of this paper are elementary.
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Communicated by Uwe Kaehler.
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Montgomery-Smith, S. Functional Calculus for Dual Quaternions. Adv. Appl. Clifford Algebras 33, 36 (2023). https://doi.org/10.1007/s00006-023-01282-y
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DOI: https://doi.org/10.1007/s00006-023-01282-y