- Computer Science 64
- Mathematics 64
- Biomedical Engineering 6
- Agriculture 3
- Earth and Atmospheric Sciences 2
- Mechanical Engineering 2
- Aeronautics and Astronautics Engineering 1
- Nuclear Engineering 1
- Physics 1

- Walter Gautschi 64
- Pavlos Vlachos 6
- Benjamin Dickerhoff 4
- David Saloner 4
- Melissa Brindise 4
- Michael Markl 4
- Sean Rothenberger 4
- Susanne Schnell 4
- Vitaliy Rayz 4
- James Krogmeier 3

- Dataset 87

10.4231/R7PN93HS

04/22/2014

The first 100 recurrence coefficients for the Freud weight function w(x)=exp(-x^4}) on R are obtained to 32 decimal digits from the first 200 moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec. 3 of "Variable-precision recu...

Computer Science Equation Table Freud polynomials Freud weight function Gaussian quadrature Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R7TD9V74

04/22/2014

The first 100 recurrence coefficients for the Freud weight function w(x)=exp(-x^8}) on R are obtained to 32 decimal digits from the first 200 moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec. 3 of "Variable-precision recu...

Computer Science Equation Table Freud polynomials Freud weight function Gaussian quadrature Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R7X63JTM

04/22/2014

The first 100 recurrence coefficients for the half-range Hermite weight function w(x)=exp(-x^2) on R_+} are obtained to 32 decimal digits from the first 200 moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec.3 of "Variable-...

Computational methods Computer Science Equation Table Gaussian quadrature Hermite weight function Hilbert Transforms Integral Transforms Mathematics Matlab Numerical integrations OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R70Z715M

04/22/2014

The first 100 recurrence coefficients for the weight function w(x)=x^-1/2}(1-x)^-1/2}log(1/x) on (0,1) are obtained to 32 decimal digits from the first 200 modified moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec.3 of "G...

Computer Science Equation Table Gauss-Radau formula Jacobi polynomials Jacobi weight functions Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R79G5JRN

04/22/2014

The first 100 recurrence coefficients for the weight function w(x)=x^-1/2}(1-x)^1/2}log(1/x) on (0,1) are obtained to 32 decimal digits from the first 200 modified moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec.3 of "Ga...

Computer Science Equation Table Gauss-Radau formula Jacobi polynomials Jacobi weight functions Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R7SF2T39

04/22/2014

The first 100 recurrence coefficients for the weight function w(x)=x^1/2}(1-x)^-1/2}log(1/x) on (0,1) are obtained to 32 decimal digits from the first 200 modified moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec.3 of "Ga...

Computer Science Equation Table Gauss-Radau formula Jacobi polynomials Jacobi weight functions Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

10.4231/R74Q7RWJ

04/22/2014

The first 100 recurrence coefficients for the weight function w(x)=x^1/2}(1-x)^1/2}log(1/x) on (0,1) are obtained to 32 decimal digits from the first 200 modified moments by using Chebyshev's algorithm in sufficiently high precision; cf. Sec.3 of "Gau...

10.4231/R7ZG6Q6T

12/30/2015

This dataset includes symbolic variable-precision versions of some of the more important OPQ routines.

Airy weight function Bose-Einstein distribution Chebyshev-type quadratures Classical weight functions Computer Science Fermi Dirac weight Function Freud weight function Gauss-type quadrature rules Hermite weight function Jacobi weight functions K-Bessel weight function Laguerre weight functions Mathematics Matlab OPQ routine Orthogonal polynomials Perl Script quadrature Software source code Walter Gautschi Archives Walter Gautschi Selected Works

10.4231/R7NK3BZ7

04/23/2014

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, infinity] and e^-1/t^2 - t^...

Computer Science Densely oscillating weight functions Exponentially decaying weight functions Gaussian quadrature Mathematics Matlab Orthogonal polynomials Walter Gautschi Archives

10.4231/R7QJ7F7V

04/23/2014

Standard numerical analysis tools, combined with elementary calculus, are deployed to evaluate a densely and wildly oscillatory integral that had been proposed as a computational problem in the''SIAM 100-Digit Challenge''. Numerical results...

Computer Science FORTRAN Gauss quadrature approximation Jacobi weight functions Mathematics Matlab Numerical Evaluation Orthogonal polynomials Oscillatory integrals Software source code Walter Gautschi Archives

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