Fueter’s theorem (1934) asserts that every holomorphic intrinsic function of one complex variable induces an axial quaternionic monogenic function. Sce (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat 23:220–225, 1957) generalizes Fueter’s theorem to the Euclidean spaces \({{\mathbb {R}}}^{n+1}\) for n being odd positive integers. By using pointwise differential computation he asserted that every holomorphic intrinsic function of one complex variable induces an axial Clifford monogenic function for the cases n being odd. Qian (Rend Mat Acc Lincei 8:111–117, 1997) extended Sce’s result to both n being odd and even cases by using the corresponding Fourier multiplier operator when the required integrability is guaranteed, and the Kelvin inversion if not. For n being odd, Qian’s generalization coincides with Sce’s result based on the pointwise differential operator. In this paper, we unify these results in the distribution sense.

Fueter定理（1934）断言，一个复杂变量的每个全纯内在函数都引起一个轴向四元离子单基因函数。SCE（姿态亚甲纳兹Lincei雷德氯科学Fis的垫纳特23：220-225，1957）概括Fueter定理到欧氏空间\（{{\ mathbb {R}}} ^ {N + 1} \）为Ñ为奇数正整数。他断言，通过使用逐点微分计算，对于n个奇数情况，一个复变量的每个全纯内在函数都会引起一个轴向Clifford单基因函数。钱（Rend Mat Acc Lincei 8：111–117，1997）将Sce的结果扩展到两个n当保证所需的可积性时，通过使用相应的傅里叶乘数运算符，可以得出奇数和偶数情况；如果不能，则使用开尔文求逆。对于n为奇数，Qian的推广与基于点微分算子的Sce的结果相符。在本文中，我们将这些结果在分布意义上加以统一。