Stephen Montgomery-Smith, Functional calculus for dual quaternions. Adv. Appl. Clifford Algebras 33, 36 (2023). We give a formula for \(f(\eta)\), where \(f :\mathbb C \to \mathbb C\) 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. This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: Use of this Accepted Version is subject to the publisher's Accepted Manuscript terms of use manuscript-terms. Springer Nature have also provided a web site with the published article here: (tex, pdf, actual article.)


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