Computing polynomials orthogonal with respect to densely oscillating and exponentially decaying weight functions and related integrals

摘要

Software (in Matlab) is developed for computing variable-precision recurrence coefficients for orthogonal polynomials with respect to the weight functions 1+sin(1/t), 1+cos(1/t), e-1/t on [0,1], as well as e-1/t-t on [0,∞] and e-1/t2-t2 on [-∞,∞]. Numerical examples are given involving Gauss quadrature relative to these weight functions.