Stephen Montgomery-Smith, Functional calculus for dual quaternions.
Adv. Appl. Clifford Algebras 33, 36 (2023). https://doi.org/10.1007/s00006-023-01282-y.
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.
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review (when applicable) but is not the Version of Record and does not reflect post-acceptance
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http://dx.doi.org/10.1007/s00006-023-01282-y. Use of this Accepted Version is subject to the publisher's Accepted
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manuscript-terms. Springer Nature have also provided a web site with the published article here: https://rdcu.be/dcVI1.
(tex, pdf, actual article.)
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