Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform belongs to $[0,1/2]$. In this paper we consider the construction of generalized Gauss-Radau quadrature rules for Hankel transform. We show that, if adding certain value and derivative information at the left endpoint, then complex generalized Gauss-Radau quadrature rules for Hankel transform of integer order can be constructed with theoretical guarantees. Orthogonal polynomials that are closely related to such quadrature rules are investigated and their existence for even degrees is proved. Numerical experiments are presented to confirm our findings.

翻译：振荡积分变换的复高斯求积法则具有能达到最优渐近阶的优势。然而，仅当变换的阶数属于$[0,1/2]$区间时，汉克尔变换的此类求积法则的存在性才能得到保证。本文研究汉克尔变换的广义高斯-拉道求积法则的构造。我们证明，若在左端点处附加特定的函数值与导数值信息，则可为整数阶汉克尔变换构造具有理论保证的复广义高斯-拉道求积法则。本文研究了与此类求积法则密切相关的正交多项式，并证明了偶数次此类多项式的存在性。数值实验验证了我们的结论。