超空间中Hermite多项式和Gegenbauer多项式的Clifford分析
Hermite and Gegenbauer polynomials in superspace using Clifford analysis
摘要：
将标准Clifford分析中的Clifford-Hermite多项式和Clifford-Gegenbauer多项式仅以象征性的方式推广到超空间Clifford分析的新框架中。这意味着人们并不先验地需要超空间中的积分理论。并证明了它的正交关系、微分方程和递推公式等基本性质。最后，讨论了超Clifford-Hermite多项式的一个有趣的物理应用，从而给出了超维数的一个解释。
英文摘要：
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
