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
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 1
Cited 2

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]

Journal of Computational and Applied Mathematics
Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity

Applied Numerical Mathematics

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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-ton [0, ∞] and e-1/t2-t2 on [-∞, ∞]. Numerical examples are given involving Gauss quadrature relative to these weight functions.