A Brief Look into the Lambert W Function

Author(s)
Thomas P. Dence

ABSTRACT

The Lambert W function has its origin traced back 250 years, but it’s just been in the past several decades when some of the real usefulness of the function has been brought to the attention of the scientific community.

The Lambert W function has its origin traced back 250 years, but it’s just been in the past several decades when some of the real usefulness of the function has been brought to the attention of the scientific community.

Cite this paper

T. Dence, "A Brief Look into the Lambert W Function,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 887-892. doi: 10.4236/am.2013.46122.

T. Dence, "A Brief Look into the Lambert W Function,"

References

[1] J. J. Gray and L. Tiling, “Johann Heinrich Lambert, Mathematician and Scientist,” Historia Mathematica, Vol. 5, No. 7, 1978, pp. 13-14. doi:10.1016/0315-0860(78)90133-7

[2] B. Hays, “Why W,” American Scientist, Vol. 93, No. 2, 2005, pp. 104-108.

[3] R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey and D. E. Knuth, “On the Lambert W Function,” Advances in Computational Mathematics, Vol. 5, No. 1, 1996, pp. 329-359.

[4] L. Euler, “De Formulis Exponentialibus Replicates,” Leonhardi Euleri Opera Omnia, Ser. 1, Opera Mathematics, Vol. 15, 1927, pp. 268-297.

[5] F. Chaspeau-Blondeau and A. Monir, “Numerical Evaluation of the Lambert W Function and Application to Generation of Generalized Gaussian Noise with Exponent ?,” IEEE Transactions on Signal Processing, Vol. 50, No. 1, 2002, pp. 2160-2165. doi:10.1109/TSP.2002.801912

[6] R. M. Corless, G. H. Gonnet, D. E. Hare and D. J. Jeffrey, “Lambert’s W Function in Maple,” The Maple Technical Newsletter, Vol. 9, 1993, pp. 12-22.

[7] F. Olver, D. Lozier, et al., “NIST Handbook of Mathematical Functions,” Cambridge University Press, Cambridge, 2010.

[8] W. Ledermann, “Handbook of Applicable Mathematics,” Vol. III, John Wiley & Sons, New York, 1981. pp. 151152.

[9] G. Alefeld, “On the Convergence of Halley’s Method,” The American Mathematical Monthly, Vol. 88, No. 7, 1981, pp. 530-536. doi:10.2307/2321760

[10] F. N. Fritsch, R. E. Shafer and W. P. Crowly, “Solution to the Transcendental Equation wew = x,” Communications of the ACM, Vol. 16, No. 2, 1973, pp. 123-124. doi:10.1145/361952.361970

[11] F. D. Parker, “Integrals of Inverse Functions,” The American Mathematical Monthly, Vol. 62, 1955, pp. 439-440. doi:10.2307/2307006

[12] F. Gouvea, Ed., “Time for a New Elementary Function?” FOCUS (Newsletter of Mathematics Association of America), Vol. 20, 2000, p. 2.

[13] E. W. Packel and D. S. Yuen, “Projectile Motion with Resistance and the Lambert W Function,” The College Mathematics Journal, Vol. 35, No. 5, 2004, pp. 337-350. doi:10.2307/4146843

[14] S. R. Valluri, D. J. Jeffrey and R. H. Corless, “Some Applications of the Lambert W Function to Physics,” Canadian Journal of Physics, Vol. 78, No. 9, 2000, pp. 823831.

[15] J. M. Borwein and R. M. Corless, “Emerging Tools for Experimental Mathematics,” The American Mathematical Monthly, Vol. 106, No. 10, 1999, pp. 889-909. doi:10.2307/2589743

[16] S. R. Cranmer, “New Views of the Solar Wind with the Lambert W Function,” American Journal of Physics, Vol. 72, No. 11, 2004, pp. 1397-1403. doi:10.1119/1.1775242

[17] D. P. Francis, K. Willson, L. C. Davies, A. J. Coats and M. Piepoli, “Quantitative General Theory for Periodic Breathing in Chronic Heart Failure and Its Clinical Implications,” Circulation, Vol. 102, No. 18, 2000, pp. 22142221. doi:10.1161/01.CIR.102.18.2214

[18] D. Kalman, “A Generalized Logarithm for ExponentialLinear Equations,” The College Mathematics Journal, Vol. 32, No. 1, 2001, pp. 2-14. doi:10.2307/2687213

[19] R. Arthur Knoebel, “Exponentials Reiterated,” The American Mathematical Monthly, Vol. 88, No. 4, 1981, pp. 235-252. doi:10.2307/2320546

[1] J. J. Gray and L. Tiling, “Johann Heinrich Lambert, Mathematician and Scientist,” Historia Mathematica, Vol. 5, No. 7, 1978, pp. 13-14. doi:10.1016/0315-0860(78)90133-7

[2] B. Hays, “Why W,” American Scientist, Vol. 93, No. 2, 2005, pp. 104-108.

[3] R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey and D. E. Knuth, “On the Lambert W Function,” Advances in Computational Mathematics, Vol. 5, No. 1, 1996, pp. 329-359.

[4] L. Euler, “De Formulis Exponentialibus Replicates,” Leonhardi Euleri Opera Omnia, Ser. 1, Opera Mathematics, Vol. 15, 1927, pp. 268-297.

[5] F. Chaspeau-Blondeau and A. Monir, “Numerical Evaluation of the Lambert W Function and Application to Generation of Generalized Gaussian Noise with Exponent ?,” IEEE Transactions on Signal Processing, Vol. 50, No. 1, 2002, pp. 2160-2165. doi:10.1109/TSP.2002.801912

[6] R. M. Corless, G. H. Gonnet, D. E. Hare and D. J. Jeffrey, “Lambert’s W Function in Maple,” The Maple Technical Newsletter, Vol. 9, 1993, pp. 12-22.

[7] F. Olver, D. Lozier, et al., “NIST Handbook of Mathematical Functions,” Cambridge University Press, Cambridge, 2010.

[8] W. Ledermann, “Handbook of Applicable Mathematics,” Vol. III, John Wiley & Sons, New York, 1981. pp. 151152.

[9] G. Alefeld, “On the Convergence of Halley’s Method,” The American Mathematical Monthly, Vol. 88, No. 7, 1981, pp. 530-536. doi:10.2307/2321760

[10] F. N. Fritsch, R. E. Shafer and W. P. Crowly, “Solution to the Transcendental Equation wew = x,” Communications of the ACM, Vol. 16, No. 2, 1973, pp. 123-124. doi:10.1145/361952.361970

[11] F. D. Parker, “Integrals of Inverse Functions,” The American Mathematical Monthly, Vol. 62, 1955, pp. 439-440. doi:10.2307/2307006

[12] F. Gouvea, Ed., “Time for a New Elementary Function?” FOCUS (Newsletter of Mathematics Association of America), Vol. 20, 2000, p. 2.

[13] E. W. Packel and D. S. Yuen, “Projectile Motion with Resistance and the Lambert W Function,” The College Mathematics Journal, Vol. 35, No. 5, 2004, pp. 337-350. doi:10.2307/4146843

[14] S. R. Valluri, D. J. Jeffrey and R. H. Corless, “Some Applications of the Lambert W Function to Physics,” Canadian Journal of Physics, Vol. 78, No. 9, 2000, pp. 823831.

[15] J. M. Borwein and R. M. Corless, “Emerging Tools for Experimental Mathematics,” The American Mathematical Monthly, Vol. 106, No. 10, 1999, pp. 889-909. doi:10.2307/2589743

[16] S. R. Cranmer, “New Views of the Solar Wind with the Lambert W Function,” American Journal of Physics, Vol. 72, No. 11, 2004, pp. 1397-1403. doi:10.1119/1.1775242

[17] D. P. Francis, K. Willson, L. C. Davies, A. J. Coats and M. Piepoli, “Quantitative General Theory for Periodic Breathing in Chronic Heart Failure and Its Clinical Implications,” Circulation, Vol. 102, No. 18, 2000, pp. 22142221. doi:10.1161/01.CIR.102.18.2214

[18] D. Kalman, “A Generalized Logarithm for ExponentialLinear Equations,” The College Mathematics Journal, Vol. 32, No. 1, 2001, pp. 2-14. doi:10.2307/2687213

[19] R. Arthur Knoebel, “Exponentials Reiterated,” The American Mathematical Monthly, Vol. 88, No. 4, 1981, pp. 235-252. doi:10.2307/2320546