第首项为非常数函数的满足Appell条件的单演多项式列
On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function
摘要：
本文的目的是构造满足Appell条件的$\mathbb R^{m+1}$中单演的$\mathbb R_{0,m}$值多项式序列$\{\mathsf{M}_n^k(x)\}_{n\ge0}$（即，序列中的每个多项式的超复数导数等于，直到乘法常数，其前项），但其首项$\mathsf{M}_0^k(x)=\mathbf{P}_k(\underline x)$是$\mathbb R_{0,m}$ -值齐次单演多项式在$\mathbb R^m$的次数为$k$，而不是像在经典的情况下常数。这个序列与所谓的Fueter定理的联系也将被讨论。
英文摘要：
In this paper we aim at constructing a sequence $\{\mathsf{M}_n^k(x)\}_{n\ge0}$ of $\mathbb R_{0,m}$-valued polynomials which are monogenic in $\mathbb R^{m+1}$ satisfying the Appell condition (i.e. the hypercomplex derivative of each polynomial in the sequence equals, up to a multiplicative constant, its preceding term) but whose first term $\mathsf{M}_0^k(x)=\mathbf{P}_k(\underline x)$ is a $\mathbb R_{0,m}$-valued homogeneous monogenic polynomial in $\mathbb R^m$ of degree $k$ and not a constant like in the classical case. The connection of this sequence with the so-called Fueter's theorem will also be discussed.
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