A new series expansion for slice regular functions (Q456760)

From the author's abstract: ``A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced by Gentili and Struppa in 2006. The basic examples of slice regular functions are the power series of type \(\sum_{n\in\mathbb N} q^n a_n\) on their balls of convergence \(B(0,R)=\{q\in H:| q|<R\}\). Conversely, if \(f\) is a slice regular function on a domain \(\Omega\subseteq H\), then it admits at each point \(q_0\in\Omega\) an expansion of type \(f(q)= \sum_{n\in\mathbb N} (q-q_0)^{*n}\), where \((q-q_0)^{*n}\) denotes the \(n\)th power of \(q-q_0\) with respect to an appropriately defined multiplication \(*\).''NEWLINENEWLINENEWLINENEWLINENEWLINE Reviewer's remark: This is a new interesting contribution of the author, after a series of papers published in good standing journals.