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

Authors:
Walter Gautschi
Affiliations:
Department of Computer Sciences, Purdue University, West Lafayette, IN 47907-2066, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

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.