In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.

在有关超复杂环境中的切片分析的文献中，有两种主要方法可在一个变量中定义切片规则函数：一种方法是要求对任何复杂平面的限制是全纯的（具有与复杂平面相同的复杂结构），第二个利用词干和词条功能。到目前为止，在几个超复杂变量的设置中，仅考虑了第二种方法，即基于茎函数的方法。在本文中，我们使用所谓的n的第一个定义维二次八角锥。这两种方法在轴对称切片域上产生相同类别的切片规则函数，但是在其他类型的域上它们却不同。我们称此类新的函数弱切片为常规切片。我们表明存在弱薄层规则函数，而在第二种方法中这些函数不是薄层规则。此外，我们研究了这些函数的各种特性，包括泰勒展开式。