论文标题
进一步研究椭圆形的Askey-Wilson多项式和相关身份的椭圆插值公式
Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities
论文作者
论文摘要
在本文中，我们介绍了所谓的椭圆形Askey-Wilson多项式，这些元素是两个特殊的Theta函数中的均质多项式。关于这种类型的多项式的重要性，我们通过矩阵反转和多项式表示的方法建立了一些一般的椭圆插值公式。此外，我们发现，通过椭圆形的ASKEY-WILSON多项式可以唯一表征椭圆形插值空间的基础。作为这些椭圆插值公式的应用，我们建立了一些新的椭圆函数认同，包括WeierStrass的Theta标识的扩展，广义的椭圆形Karlsson-Minton类型标识以及Gasper的椭圆形类似物的椭圆形类似物，用于Gasper的汇总套件的汇总，用于非常好的$ {}}} _ {6+2m} $ {6+2m} $ {6+2m} c {5+2m}
In this paper, we introduce the so-called elliptic Askey-Wilson polynomials which are homogeneous polynomials in two special theta functions. With regard to the significance of polynomials of such kind, we establish some general elliptic interpolation formulas by the methods of matrix inversions and of polynomial representations. Furthermore, we find that the basis of elliptic interpolation space due to Schlosser can be uniquely characterized via the elliptic Askey-Wilson polynomials. As applications of these elliptic interpolation formulas, we establish some new elliptic function identities, including an extension of Weierstrass' theta identity, a generalized elliptic Karlsson-Minton type identity, and an elliptic analogue of Gasper's summation formula for very-well-poised ${}_{6+2m}ϕ_{5+2m}$ series.
