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

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 / t 2 - t 2 on [ - ∞ , ∞ ] . Numerical examples are given involving Gauss quadrature relative to these weight functions.