The Lambert W-functions and some of their integrals: A case study of high-precision computation

Numerical Algorithms

Volumn 57, Issue 1, 2011, Pages 27-34

  Gautschi, Walter ^a  

^a Purdue University   (United States)

Author keywords

Integrals of Lambert W functions; Lambert W functions; Nonstandard Gaussian quadrature; Variable precision computation

Indexed keywords

EID: 79953741618     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-010-9409-6     Document Type: Article

References (8)

1. Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions. National Bureau of Standards, Applied Mathematics Series 55, U. S. Government Printing Office, Washington, DC (1964).
2. Barry, D. A., Li, L., Jeng, D.-S.: Comments on numerical evaluation of the Lambert W-functions and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Trans. Signal Process. 52, 1456-1458 (2004).
3. Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., Knuth, D. E.: On the Lambert W-functions. Adv. Comput. Math. 5, 329-359 (1996).
4. Corless, R. M., Jeffrey, D. J., Knuth, D. E.: A sequence of series for the Lambert W-functions. In: Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), pp. 197-204. ACM, New York (1997, electronic).
5. Gautschi, W.: Numerical Analysis: An Introduction. Birkhäuser, Boston (1997).
6. Gautschi, W.: Variable-precision recurrence coefficients for non-stand-ard orthogonal polynomials. Numer. Algorithms 52, 409-418 (2009).
7. Gradshteyn, I. S., Ryzhik, I. M.: Table of integrals, series, and products, 7th edn. Elsevier/Academic Press, Amsterdam (2007).
8. Yu, Y.: Personal communication, October (2009).