Chapter 1

A Twisted Tail

Dirk Laurie

Problem 1

1.1 A First Look · 1.2 Oscillatory Integrals in General · 1.3 This Particular Oscillatory Integral · 1.4 Complex Integration · 1.5 Lambert's W Function · 1.6 Transformation to a Semi-Infinite Interval · 1.7 Representation as a Divergent Series · 1.8 Transformation to a Fourier Integral · 1.9 Going for 10,000 Digits

Solution is known to more than 10,002 digits.

Code

• Mathematica
   
  • Session: p. 28
  • Figures: 1.1–1.7
     
• MATLAB
   
  • Session: p. 21 (as alternative to Octave, needs command func)
  • Lambert's W function
     
• Octave (download Octave)
   
  • Code for Tables 1.1-1.3 and Figures 1.1-1.7
  • Session: p. 21
  • Lambert's W function
     
• PARI/GP (download PARI/GP)
   
  • Session: p. 22
  • Lambert's W function
  • Ooura-Mori quadrature (and its application to Problem 1)

Links

• Walter Gautschi. The Numerical Evaluation of a Challenging Integral. Manuscript, Purdue University, 2005.
   
• Robert Corless. Lambert's W function.
   
• Brian Hayes. Why W? American Scientist 93 (2005), pp. 104–108.

• ProductLog (Lambert Function). From functions.wolfram.com―A Wolfram Web Resource.
   
• Eric W. Weisstein. Lambert W-Function. From MathWorld―A Wolfram Web Resource.

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: 07/14/05 15:42 +0200 (FB)