关于广义Gauss-Radau和Gauss-Lobatto公式的Gautschi猜想
On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae
AI总结：
本文证明了Gautschi提出的广义Gauss-Radau和Gauss-Lobatto公式中权重的正性，从而证实了Gautschi的猜想，并建立了这些求积公式的收敛定理。
摘要：
最近，Gautschi引入了所谓的广义Gauss-Radau和Gauss-Lobatto公式，这些是高斯型求积公式，不仅涉及函数在端点的值，还涉及导数。在本文中，我们证明了相应权重的正性；这一正性已被Gautschi猜想。作为结果，我们建立了这些求积公式的几个收敛定理。
英文摘要：
Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we show the positivity of the corresponding weights; this positivity has been conjectured already by Gautschi. As a consequence, we establish several convergence theorems for these quadrature formulae.
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。
