In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev algorithm, here we present a very stable algorithm based on the preconditioning of the moment matrix. Numerical experiments are provided and a geophysical application is considered.

翻译：在这项工作中,我们为涉及第一种分数功率、指数和贝塞尔函数的重量函数制定了高斯象形规则。除了基于使用标准和修改的Chebyshev算法的计算之外,我们这里还基于瞬间矩阵的前提条件提出了一个非常稳定的算法。提供了数值实验,并考虑了地球物理应用。