Chapter 9

Gradus ad Parnassum

Dirk Laurie

Problem 9

9.1 A First Look · 9.2 Accurate Evaluation of the Integral · 9.3 The Maximization Problem · 9.4 Double-Exponential Formulas · 9.5 Transformation to a Fourier Integral · 9.6 An Analytical Surprise · 9.7 Accurate Numerical Differentiation

Solution is known to more than 10,002 digits.

Code

• Mathematica
   
  • Session: p. 194
  • Figures: 9.1–9.5
     
• Maple
   
  • Session: p. 194
     
• Octave (download Octave)
   
  • Code for Tables 9.1-9.3
  • Sessions: p. 183, 189, 193
  • supporting code: prob9.m, p9G.m
  • Ooura-Mori quadrature
  • digamma (psi) function (Paul Godfrey's implementation)
     
• PARI/GP (download PARI/GP)
   
  • Solving Problem 9 to 14,000 digits (method of §9.7)

Links

• Takuya Ooura: Almighty Quadrature―C and FORTRAN routines for double-exponential quadrature.
   
• Meijer G Function. From functions.wolfram.com―A Wolfram Web Resource.
   
• Eric W. Weisstein. Meijer G Function. From MathWorld―A Wolfram Web Resource.

Supplements

• Folkmar Bornemann. How Mathematica and Maple Get Meijer's G-function into Problem 9. Note of Feb 8, 2005.

Errata

• What Figure 9.2 (left) should have looked like.

This is a web page for the book:

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing. Society of Industrial and Applied Mathematics (SIAM), Philadelphia, 2004.

last modified: 02/09/05 10:51 +0100 (FB)