论文标题
二面体类型的广义贝塞尔函数：表达作为一系列汇合角函数和拉普拉斯型积分表示
Generalized Bessel functions of dihedral-type: expression as a series of confluent Horn functions and Laplace-type integral representation
论文作者
论文摘要
在本文的第一部分中，我们表达了与二面体系统相关的广义贝塞尔函数，并且恒定的多重性函数是一系列无限的汇合角函数。导致该表达的关键要素是作者在先前论文中证明了涉及涉及gegenbauer多项式的身份的扩展，以及将泊松内核用于这些多项式的延伸。特别是，我们在标准单纯胶上得出了该广义贝塞尔函数的整体表示。本文的第二部分涉及其中一个变量的二面体系统和边界值。仍然假设多样性函数是恒定的，我们获得了相应的广义贝塞尔函数的拉普拉斯型积分表示，该函数甚至扩展到所有二面体系统的特殊实例。
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this expression is an extension of an identity involving Gegenbauer polynomials proved in a previous paper by the authors, together with the use of the Poisson kernel for these polynomials. In particular, we derive an integral representation of this generalized Bessel function over the standard simplex. The second part of this paper is concerned with even dihedral systems and boundary values of one of the variables. Still assuming that the multiplicity function is constant, we obtain a Laplace-type integral representation of the corresponding generalized Bessel function, which extends to all even dihedral systems a special instance of the Laplace-type integral representation proved in \cite{Amr-Dem}.
