论文标题
切片常规功能的球形系数
Spherical coefficients of slice regular functions
论文作者
论文摘要
鉴于Quaternionic片常规功能$ f $，我们提供了一种直接有效的方法来计算其球形扩展的系数。此类系数是根据函数本身的球形和切片衍生物获得的。之后，我们将$ f $的系数与其切片衍生品$ \ partial_ {c} f $获得的系数进行了比较，从而获得了任何因任何切片的常规功能而满足的可数差分方程式。结果在所有细节中得到证明，并伴随着几个示例。 对于某些结果，我们还提供了其他证据。
Given a quaternionic slice regular function $f$, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of $f$ with those of its slice derivative $\partial_{c}f$ obtaining a countable family of differential equations satisfied by any slice regular function. The results are proved in all details and are accompanied to several examples. For some of the results, we also give alternative proofs.
