Datasets

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subject: Computer Science creator: Walter Gautschi type: dataset

Total is 28 Results
32-digit values of the first 100 recurrence coefficients relative to the Theodorus weight function w(x)=x^{1/2}/(e^x-1) on R_{+} computed by the routine sr_theodorus(100,32)

10.4231/R71Z4290

Walter Gautschi

04/22/2014

The first 100 recurrence coefficients for orthogonal polynomials relative to the Theodorus weight function w(x)=x^(1/2)/(e^x-1) on R_+} are obtained from the first 200 moments mu_k=Gamma(k+3/2) * zeta(k+3/2), k=0,1,2,...,199, by using Chebyshev's algo...

Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

28-digit values of the recursion coefficients relative to the Airy weight function w(x)= frac{2^{2/3}pi}{3^{5/6}Gamma(2/3)} *x^{-2/3}exp(-x)Ai((3x/2)^{2/3}) on [0,infty]

10.4231/R7QN64N5

Walter Gautschi

03/21/2014

The first 40 recursion coefficients for the Airy weight function are obtained to 28 decimal digits by a discretization procedure described in Sec. 4.2 of Walter Gautschi, "Computation of Bessel and Airy functions and of related Gaussian quadrature formula...

Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

28-digit values of the recursion coefficients relative to the Bessel weight function w(x)=frac{sqrt{3}}{pi}K_{1/3}(x) on [0,infty]

10.4231/R7JW8BS2

Walter Gautschi

04/22/2014

The first 40 recursion coefficients for the Bessel weight function are obtained to 28 decimal digits by a discretization procedure described in Sec. 4.1 of Walter Gautschi, "Computation of Bessel and Airy functions and of related Gaussian quadrature formul...

Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 beta coefficients relative to the Freud weight function w(x)=exp(-x^4) computed on R by the SOPQ routine sr_freud(100,0,4,32)

10.4231/R7PN93HS

Walter Gautschi

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 Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 beta coefficients relative to the Freud weight function w(x)=exp(-x^6) computed on R by the SOPQ routine sr_freud(100,0,6,32)

10.4231/R7Z60KZ0

Walter Gautschi

04/22/2014

The first 100 recurrence coefficients for the Freud weight function w(x)=exp(-x^6}) 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 Mathematics Modification algorithms for orthogonal polynomials moment-based method Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 beta coefficients relative to the Freud weight function w(x)=exp(-x^8) computed on R by the SOPQ routine sr_freud(100,0,8,32)

10.4231/R7TD9V74

Walter Gautschi

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 Mathematics Modification algorithms for orthogonal polynomials moment-based method Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 recurrence coefficients relative to the half-range Hermite weight function w(x)=exp(-x^2) on R_{+} computed by the SOPQ routine sr_halfrangehermite(100,32)

10.4231/R7X63JTM

Walter Gautschi

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-...

Computer Science Mathematics Modification algorithms for orthogonal polynomials moment-based method Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 recurrence coefficients relative to the weight function w(x)=x^{-1/2}(1-x)^{1/2}log(1/x) on (0,1) computed by the SOPQ routine sr_jacobilog1(100,-1/2,1/2,32)

10.4231/R79G5JRN

Walter Gautschi

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 Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 recurrence coefficients relative to the weight function w(x)=x^{1/2}(1-x)^{1/2}log(1/x) on (0,1) computed by the SOPQ routine sr_jacobilog1(100,1/2,1/2,32)

10.4231/R74Q7RWJ

Walter Gautschi

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...

Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

LAMBERTW: Matlab programs for evaluating the Lambert W-functions and some of their integrals

10.4231/R7Z31WJP

Walter Gautschi

04/23/2014

The real-valued Lambert W-functions considered here are w_0(y) and w_-1}(y), solutions of we^w = y, -1/e < y < 0, with values respectively in (-1/e < y <0) and (-infinity, -1).

Binet-like weight functions Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Walter Gautschi Archives weight functions

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