论文标题
Clifford Legendre多项式的特性
Properties of Clifford Legendre Polynomials
论文作者
论文摘要
Clifford-Legendre和Clifford-Gegenbauer多项式是对某些差异操作员的特征函数，这些差异操作员在$ m $ diperional-demensional Euclidean space $ {\ Mathbb r}^m $上定义的功能，并在相关的Clifford algebra $ {\ Mathbb r $ $ $ $ $ $ $ $ $ $ $ $ $ $ $中占据价值。这些多项式的新复发和引擎盖类型公式被证明，因为它们的傅立叶变换是计算的。给出了从球形单基因和雅各比多项式方面的明确表示，其后果包括零的交织。在$ m = 2 $的情况下，我们描述了偶数和奇数多项式之间的变性。
Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra ${\mathbb R}_m$. New recurrence and Bonnet type formulae for these polynomials are proved, as their Fourier transforms are computed. Explicit representations in terms of spherical monogenics and Jacobi polynomials are given, with consequences including the interlacing of the zeros. In the case $m=2$ we describe a degeneracy between the even- and odd-indexed polynomials.
