A new series expansion for slice regular functions

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 ∑n∈Nqnan∑n∈Nqnan on their balls of convergence B(0,R)={q∈H:|q|