References on the Lambert W function and its generalizations
Here you can find a compilation of references on the Lambert W function, its generalizations, and applications. It is by no means a complete list, but with common effort, it can grow further.
The articles appear in reverse chronological order inside their sections. If there are links to PDFs, they exclusively point to freely available content.
If you are interested in numerical approximations and computational aspects of the W function, you can search the papers marked with (n). Papers on inequalities regarding W are marked with (i). Just use the search function of your browser to jump easily to these papers.
Please send your suggestions and info on left-out articles here: istvanmezo81@gmail.com. If you send me a new citation, please format it beforehand like the below references (for journal articles: author(s), title, journal volume(issue) (year), first page-last page.).
1. References on the classical Lambert W function
Baisheng Wu et al., Analytical approximations to the Lambert W function, Applied Math. Modelling 104 (2022), 114-121. (n)
L. Lóczi, Guaranteed- and high-precision evaluation of the Lambert W function, Appl. Math. Comput. 433 (2022), 1-22. pdf (n)
F. Johansson, Computing the Lambert W function in arbitrary-precision complex interval arithmetic, Numerical Algorithms 83 (2020), 221-242. pdf of the version published on HAL Archives (n)
H. Vazquez-Leal, M. A. Sandoval-Hernandez, J. L. Garcia-Gervacio, A. L. Herrera-May, U. A. Filobello-Nino, PSEM Approximations for Both Branches of Lambert W Function with Applications, Hindawi Discrete Dynamics in Nature and Society, Volume 2019 (2019), Article ID: 8267951. pdf (n)
F. Alzahrani, A. Salem, Sharp bounds for the Lambert W function, Integral Transf. Spec. Funct. 29(12) (2018), 971-978. (i)
C. B. Corcino, R. B. Corcino, I. Mező, Continued fraction expansions for the Lambert W function, Aeq. Math. 93 (2019), 485-498. (n)
A. Kheyfits, Another incarnation of the Lambert W function, ArXiv, 2017. pdf
H. al Kafri, D. J. Jeffrey, R. M. Corless, Rapidly Convergent Integrals and Function Evaluation, MACIS 2017, p. 270-274.
R. Iacono, J. P. Boyd, New approximations to the principal real-valued branch of the Lambert W-function, Adv. Comput. Math. 43 (2017), 1403-1436. pdf at Resarchgate (n)
D. J. Jeffrey, N. Murdoch, Stirling Numbers, Lambert W and the Gamma function, MACIS 2017, 275-279.
D. J. Jeffrey, Branch Structure and Implementation of Lambert W, Math. Comput. Sci. 11 (2017), 341-350. (n)
J. M. Borwein, S. B. Lindstrom, Meetings with Lambert W and Other Special Functions in Optimization and Analysis, Online J. Pure Appl. Funct. Anal 1(3) (2016), 361-396. pdf
M. Josuat-Vergès, Derivatives of the tree function, Ramanujan J. 38 (2015), 1-15.
R. M. Corless, J.-R. Hu, D. J. Jeffrey, Some definite integrals containing the Tree T function, ACM Communications in Computer Algebra 48(2) (2014), 33-41. pdf
D. J. Jeffrey, J. E. Jankowski, Branch differences and Lambert W, SYNASC '14, 2014. pdf
J. L. González-Santander, G. Martín, Some remarks on the self-exponential function: Minimum value, inverse function, and indefinite integral, Int. J. Anal. 2014 (2014), Article ID:195329. pdf
T. P. Dence, A Brief Look into the Lambert W Function, Applied Mathematics 4 (2013), 887-892. pdf
T. Fukushima, Precise and fast computation of Lambert W-functions without transcendental function evaluations, J. Comput. Appl. Math. 244 (2013), 77-89. pdf (n)
T. C. Scott, G. Fee, J. Grotendorst, Asymptotic series of generalized Lambert W function, ACM Communications in Computer Algebra 47(3) (2013), 75-83. (n)
G. A. Kalugin, D. J. Jeffrey, R. M. Corless, Bernstein, Pick, Poisson and related integral expressions for Lambert W, Integral Transf. Spec. Funct. 23(11) (2012), 817-829. pdf
D. Veberič, Lambert W function for applications in physics, Computer Physics Communications 183 (2012), 2622-2628. This paper had previously been named before its final publication as "Having fun with the Lambert W(x) function" (see on ArXiv) (n)
G. A. Kalugin, D. J. Jeffrey, Convergence in C of series for the Lambert W Function, ArXiv, 2012. pdf
G. A. Kalugin, D. J. Jeffrey, R. M. Corless, P. M. Borwein, Stieltjes and other integral representations for functions of Lambert W, Integral Trans. Spec. Funct. 23(8) (2012), 581-593.
G. A. Kalugin, D. J. Jeffrey, Unimodal sequences show that Lambert W is Bernstein, C. R. Math. Rep. Acad. Sci. Canada Vol. 33 (2) (2011), 50-56. pdf
G. A. Kalugin, D. J. Jeffrey, Series transformations to improve and extend convergence, in:Lecture Notes in Computer Science, vol 6244. Springer, 2010. pdf
S. Yi, P. W. Nelson, A. G. Ulsoy, Time-Delay Systems - Analysis and Control Using the Lambert W function, World Scientific, 2010.
S. M. Stewart, On certain inequalities involving the Lambert W function, JIPAM 10(4) (2009), Article 96. pdf (i)
P.B. Brito, F. Fabião, A. Staubyn, Euler, Lambert, and the Lambert W function today, Math. Sci. 33 (2008), 127–133.
M. Bronstein, R. M. Corless, J. H. Davenport, D. J. Jeffrey, Algebraic properties of the Lambert W function from a result of Rosenlicht and of Liouville, Integral Transf. Spec. Funct. 19(10) (2008), 709-712. pdf
A. Hoorfar, M. Hassani, Inequalities on the Lambert W function and hyperpower function, JIPAM 9(2) (2008), Article 51. pdf (i)
A.E. Dubinov, I.D. Dubinova, S.K. Saikov, The Lambert W-function and its applications to mathematical problems of physics, The Russian Federal Nuclear Center, Sarov, Russia, 2006 (in Russian)
B. Hayes, Why W?, American Scientist 93 (2005), 104-108.
A. Kheyfits, Closed form representations of the Lambert W function, Fractional Calculus and Applied Analysis 7(2) (2004), 177-190. pdf
R. M. Corless, D. J. Jeffrey, On the Wright ω function, AISC 2002. pdf
F. Chapeau-Blondeau, A. Monir, Numerical Evaluation of the Lambert W Function and Application to Generation of Generalized Gaussian Noise With Exponent 1/2, IEEE Transactions on Signal Processing 50(9) (2002), 2160-2165. pdf (n)
J. M. Borwein, R. M. Corless, Emerging tools for experimental mathematics, Amer. Math. Monthly 106(10) (1999), 889-909.
R. M. Corless, D. J. Jeffrey, Graphing elementary Riemann surfaces, SIGSAM Bulletin 32(1) (1998), 11-17.
J. P. Boyd, Global approximations to the principal real-valued branch of the Lambert W-function, Appl. Math. Lett. 11(6) (1998), 27-31. pdf (n)
R. M. Corless, D. J. Jeffrey, D. E. Knuth, A sequence of series for the Lambert W function, ISSAC '97, 197-204. pdf
D. J. Jeffrey, D. E. G. Hare, R. M. Corless, Unwinding the branches of the Lambert W function, Math. Scientist 21(1) (1996), 1-7. pdf
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, On the Lambert W function, Adv. Comput. Math. 51 (1996), 329-359. pdf
D. J. Jeffrey, R. M. Corless, D. E. G. Hare, D. E. Knuth, On the inversion of yαey in terms of associated Stirling numbers (1995), ArXiv. pdf
B. Salvy, Fast computation of some asymptotic functional inverses, J. Symbolic Comput. 17 (1994), 227-236. pdf (n)
F. N. Fritsch, R. E. Shafer, W. P. Crowley, Solution of the transcendental equation we^w = x, Communications of the ACM 16(2) (1973) pdf (n)
2. References on applications of the classical Lambert function
2.a Physics
P. M. Jordan, Poroacoustic solitary waves under the unidirectional Darcy–Jordan model, Wave Motion 94 (2020), Article 102498. See also the addendum.
A. E. Dubinov, Mathematical tricks for pseudopotentials in the theories of nonlinear waves in plasmas, Phys. Plasmas 29 (2022), Article 020901. full text
A. Maignan, L. P. Reddy, S. Jeevanandam, P. C. Deshmukh, K. Roberts, N. Jisrawi, S. R. Valluri, The electronic properties of graphene nanoribbons and the offset logarithm function, Materials Today: Proceedings (in press)
I. Mező, C. B. Corcino, R. B. Corcino, Resolution of the Plane-symmetric Einstein-Maxwell fields with a generalization of the Lambert W function, J. Phys. Commun. 4 (2020) Article no.: 085008.
Bharatbhai, P C Deshmukh, R. B Scott, K. Roberts, S. R. Valluri, Lambert W function methods in double square well and waveguide problems, J. Phys. Commun 4(6) (2020), 065001. full text
A. Al Mamon, S. Saha, Testing Lambert W equation of state with observational Hubble parameter data (2020) arXiv
A. Tchorbadjieff, P. Mayster, Geometric branching reproduction Markov processes, Modern Stoch. Theory Appl. (2020), 1-22. full text
S. Saha, K. Bamba, The Lambert W function: A newcomer in the Cosmology class?, Zeitschrift für Naturforschung A 75(1) (2019), 23-27. arXiv
R. B. W. Tekam, J. Kengne, G. D. Kenmoe, High frequency Colpitts’ oscillator: A simple configuration for chaos generation, Chaos, Solitons and Fractals 126 (2019), 351-360.
H. H. Bauschke, S. B. Lindstrom, Proximal averages for minimization of entropy functionals, 2018 arXiv
O. Olendski, Thermodynamic properties of the 1D Robin quantum well, Ann. Phys. 530(8) (2018), 1700325
S. Rebollo-Perdomo, C. Vidal, Bifurcation of limit cycles for a family of perturbed Kukles differential systems, American Institute of Mathematical Sciences, Discrete \& Continuous Dynamical Systems-A 38(8) (2018), 4189-4202. pdf
M. Saillenfest, B. Tabone, E. Behar, Solar wind dynamics around a comet - The paradigmatic inverse-square-law model, Astronomy & Astrophysics 617 (2018), Article number: A99. arXiv
R. M. Digilov, Gravity discharge vessel revisited: An explicit Lambert W function solution, Amer. J. Phys. 85 (7) (2017), 510-514.
J. Guo, Exact procedure for Einstein–Johnson’s sidewall correction in open channel flow, J. Hydraul. Eng. 143(4) (2016).
C. H. Belgacem, Explicit solution for critical thickness of semicircular misfit dislocation loops in strained semiconductors heterostructures, Silicon 8 (2016), 397-399.
K. Roberts, S. R. Valluri, Tutorial: The quantum finite square well and the Lambert W function, Canad. J. Phys. 95(2) (2016), 105-110.
S. Sharma, P. Shokeen, B. Saini, S. S. Chetna, J. Kashyap, R. Guliani, S. Sharma, U.M. Khanna, A. Jain, A. Kapoor, Exact analytical solutions of the parameters of different generation real solar cells using Lambert W−function: a review article, Int. J. Renew. Energy 4 (2014), 155–194.
D. Jaisson, Simple formula for the wave number of the Goubau line, Electromagnetics 34 (2014), 85-91.
P. M. Jordan, A note on the Lambert W-function: applications in the mathematical and physical sciences, Contemporary Mathematics 618 (2014), 247-263.
C. S. Alonso, Black holes in supergravity with applications to string theory, PhD thesis, Universidad Autonoma de Madrid, 2013. pdf
A. E. Dubinov, Exactly solved models of ionization equilibrium of thermal plasmas with multicharged ions, IEEE Trans. Plasma Sci. 41(3) (2013), 425-436.
A. Houari, Additional applications of the Lambert W function in physics, Eur. J. Phys. 34 (2013), 695-702.
A. E. Dubinov, D. Yu. Kolotkov, Ion-acoustic super solitary waves in dusty multispecies plasmas, IEEE Trans. Plasma Sci. 40(5) (2012), 1429-1433.
A. E. Dubinov, L. A. Senilov, Generalized Bohm criterion for a multicomponent plasma, Technical Physics 57(8) (2012), 1090–1094.
S. M. Stewart, On the trajectories of projectiles depicted in early ballistic woodcuts, European Journal of Physics, 33(1) (2012), 149–166.
C. H. Belgacem, M. Fnaiech, Solution for the critical thickness models of dislocation generation in epitaxial thin films using the Lambert W function, J. Mater. Sci. 46 (2011), 1913-1915.
C. H. Belgacem, M. Fnaiech, Exact analytical solution for the critical layer thickness of a lattice-mismatched heteroepitaxial layer, J. Electronic Materials 39(10) (2010), 2248-2250.
D. Clamond, Efficient resolution of the Colebrook equation, Ind. Eng. Chem. Res. 48 (2009), 3665-3671.
S. R. Valluri, M. Gil, D. J. Jeffrey, S. Basu, The Lambert W function and quantum statistics, J. Math. Phys. 50 (2009), Article no.: 102103. pdf
V. A. Gordienko, A. E. Dubinov, Principle of charge–mass invariance of motion and possibility of steady-state solitary electrostatic waves in a nearly symmetric plasma, Technical Physics 53(1) (2008), 43–48.
P. Sengupta, The Lambert W function and solutions to Kepler’s equation, Celestial Mech Dyn Astr 99 (2007), 13-22.
B. Alterkop, I. D. Dubinova, A. E. Dubinov, and R. L. Boxman, The double sheath at the plasma-wall boundary, Contrib. Plasma Phys. 47(3) (2007), 190–201.
A. E. Dubinov, A. A. Dubinova, Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons, Plasma Physics Reports 33(10) (2007), 859–870.
A. E. Dubinov, I. N. Galidakis, Explicit solution of the Kepler equation, Physics of Particles and Nuclei Letters 4(3) (2007), 213–216.
B. A. Alterkorp, I. D. Dubinova, A. E. Dubinov, Charged double layer at the boundary between a symmetric plasma and a wall, Technical Physics 52(7) (2007), 884–891.
B. A. Alterkorp, I. D. Dubinova, A. E. Dubinov, Structure of the charged sheath at the plasma–charged body boundary, Journal of Experimental and Theoretical Physics 102(1) (2006), 173–181.
A. E. Dubinov, I. D. Dubinova, Exact solution of the Landau dispersion equation for electron plasma oscillations, Technical Physics Letters 32(1) (2006), 36–37.
V. A. Gordienko, I. D. Dubinova, A. E. Dubinov, Nonlinear theory of large-amplitude stationary solitary waves in symmetric unmagnetized e-e+ and C_60-C_60+ plasmas, Plasma Physics Reports 32(11) (2006), 910–915.
A. E. Dubinov, I. D. Dubinova, S. K. Saĭkov, The Lambert W function and its applications to mathematical problems of physics. RFNC-VNIIEF: Sarov, 2006.
S. M. Stewart, An analytic approach to projectile motion in a linear resisting medium, International Journal of Mathematical Education in Science and Technology, 37(4) (2006), 411–431.
D. A. Morales, Exact expressions for the range and the optimal angle of a projectile with linear drag, Canad. J. Phys. 83(1) (2005), 67-83.
A. E. Dubinov, I. D. Dubinova, How can one solve exactly some problems in plasma theory, J. Plasma Physics 71(5) (2005), 715-728.
B. V. Alekseev, A. E. Dubinov, I. D. Dubinova, Analytical and numerical solutions of generalized dispersion equations for one-dimensional damped plasma oscillation, High Temperature. 43(4) (2005), 479–485.
S. M. Stewart, Linear resisted projectile motion and the Lambert W function, American Journal of Physics, 73(3) (2005), 199.
S. R. Cranmer, New views of the solar wind with the Lambert W function, Am. J. Phys. 72(11) (2004), 1397-1403. arXiv
A. E. Dubinov, I. D. Dubinova, Exact value of conjugate ion current in an electrolyte in the Gurevich–Kharkats diffusion-migration model, Technical Physics 49(11) (2004), 1512–1513.
A. E. Dubinov, Dynamics of virtual-cathode formation in a viscous-friction medium, Doklady Physics 49(12) (2004), 697–700.
I. D. Dubinova, Application of the Lambert W function in mathematical problems of plasma physics, Plasma Physics Reports, 30(10) (2004), 872–877.
A. E. Dubinov, I. D. Dubinova, S. K. Saĭkov, An exact solution to the problem of combustion wave propagation, Doklady Physics 49(2) (2004), 132–133.
A. E. Dubinov, I. D. Dubinova, and S. K. Saĭkov, An exact solution to the problem of combustion wave propagation, Doklady Physics 49(2) (2004), 132–133.
D. C. Jenn, Applications of the Lambert W function in electromagnetics, IEEE Antenna's and Propagation Magazine 44(3) (2002), 139-142. pdf
F. Chapeau-Blondeau, Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2, IEEE Transactions on signal processing 50(9) (2002), 2160-2165. (n) pdf
S. R. Valluri, D. J. Jeffrey, R. M. Corless, Some applications of the Lambert function to physics, Can. J. Physics 78(9) (2000), 823-831. pdf
S. A. Campbell, Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops, Dynam. Contin. Discrete Impuls. Systems 5 (1999), 225-235.
2.b Analytic number theory
G. França, A. LeClair, Transcendental equations satisfied by the individual zeros of Riemann zeta, Dirichlet and modular L-functions, Comm. Num. Theor. Phys. 9(1) (2015), 1-50. pdf
2.c Probability theory, Statistics, Optimization
H. Nakashima, P. Graczyk, Stieltjes transforms and R-transforms associated with two-parameter Lambert–Tsallis functions, Entropy 25 (2023), 858-878. pdf
A. G. Pakes, Affine relation between an infinitely divisible distribution function and its Lévy measure, J. Math. Anal. Appl. 499(2) (2021), Article no. 125008.
A. G. Pakes, Self-decomposable laws from continuous branching processes, J. Theor. Probab. 33 (2020), 361-395.
X.-Ke Wu, J. Qin, W.-X. Qu, Yi-J. Zeng, X. S. Yang, Collaborative optimization of dynamic pricing and seat allocation for high-speed railways: An empirical study from China, IEEE Access, 10.1109/ACCESS.2019.2943229
A. G. Pakes, The Lambert W function, Nuttall’s integral, and the Lambert law, Statistics and Probability Letters 119 (2018), 53-60.
P. Jodrá, M. D. Jiménez-Gamero, A note on the Log-Lindley distribution, Insrance: Mathematics and Economics 71 (2016), 189-194.
A. Gasull, M. Jolis, F. Utzet, On the norming constants for normal maxima, J. Math. Anal. Appl. 422(1) (2015), 376-396. pdf
B. Bolker, Rogers random predator equation: extensions and estimation by numerical integration, 2012 manuscript
G. M. Goerg, Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation, Ann. Appl. Stat. 5(3) (2011), 2197-2230.
M. Molli, K. Venkataramaniah, S. R. Valluri, The polylogarithm and the Lambert W functions in thermoelectrics, Can. J. Phys. 89 (2011), 1171–1178. pdf
A. G. Pakes, Lambert’sW, infinite divisibility and Poisson mixtures, J. Math. Anal. Appl. 378 (2011), 480-492.
P. Jodrá, Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function, Math. Comput. Simulations 81(4) (2010), 851-859.
C. Tellambura, D. Senaratne, Accurate Computation of the MGF of the Lognormal Distribution and its Application to Sum of Lognormals, IEEE Transactions on Communications (2010), 1568-1577.
M. Stehlík, Distributions of exact tests in the exponential family, Metrika 57 (2003), 145-164.
2.d Difference, differential and delay differential equations
M. Sherman, G. Kerr, G. González-Parra, Analytic solutions of linear neutral and non-neutral delay differential equations using the Laplace transform method: featuring higher order poles and resonance, Journal of Engineering Mathematics 140 (2023), Article no. 12.
H. Moradian, S. S. Kia, A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback, IEEE Transactions on Control of Network Systems 10(1) (2022), 157-168.
G. Kerr, G. González-Parra, Accuracy of the Laplace transform method for linear neutral delay differential equations, Math. Comput. Simulation 197 (2022), 308-326.
H. Moradian, S. S. Kia, On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems, IEEE Transactions on Automatic Control 65(11) (2019), 4832-4839.
S. Yi, S.Duan, P. W. Nelson, A. G. Ulsoy, The Lambert W Function Approach to Time Delay Systems and the LambertW_DDE Toolbox, IFAC Proceedings 45(14) (2012), 114-119. pdf
L. Wetzel, Effect of distributed delays in systems of coupled phase oscillators. PhD thesis, Max Planck Institute of Complex Systems, 2012.
B. Cogan, A. M. de Paor, Analytic root locus and Lambert W function in control of a process with time delay, J. Electrical Engng. 62(6) (2011), 327-334. pdf on the webpage of the journal
S. Yi, Time-delay systems: analysis and control using the Lambert W function. PhD thesis, University of Michigan, 2009.
H. Shinozaki, Lambert W Function approach to stability and stabilization problems for linear time-delay systems, PhD thesis Kyoto Institute of Technology, 2007. pdf
C. Hwang, Yi-Ch. Cheng, Use of Lambert W function to stability analysis of time-delay systems, Proceedings of the American Control Conference 41(11) (2005), 4283-4288.
A. E. Dubinov, I. D. Dubinova, S. K. Saikov, Characteristic roots and stability domains of one dynamic delay system, Automation and Remote Control 66(8) (2005), 1212-1213.
I. D. Dubinova, Exact closed-form solutions of some nonlinear differential equations, Differential Equations, 40(8) (2004), 1195–1196.
2.e Networks, communication, signal processing
A. Hanif, M. Doroslovački, Simultaneous Terahertz imaging with information and power transfer (STIIPT), IEEE Journal of Selected Topics in Signal Processing, Early Access
H.-N. Teodorescu, Noise equilibrium frequency as a measure of the low noise devices quality involves the Lambert function, 7th International Symposium on Electrical and Electronics Engineering (ISEEE), 2021
I. Chatzigeorgiou, Bounds on the Lambert function and their application to the outage analysis of user cooperation, IEEE Communications Letters 17(8) (2013), 1505-1508.
D. Wu, Y. Cai, L. Zhou, A Cooperative Communication Scheme Based on Coalition Formation Game in Clustered Wireless Sensor Networks, IEEE Transactions on Wireless Communications 11(3) (2012), 1190-1200.
F. Brah, A. Zaidi, J. Louveaux, L. Vandendorpe, On the Lambert-W function for constrained resource allocation in cooperative networks, EURASIP Journal on Wireless Communications and Networking, 2011, article no: 19. pdf
F. Brah, L. Vandendorpe, V. Ramon, A tractable method for constrained resource sharing in OFDMA wireless mesh networks, IEEE ICC 2010 proceedings
F. Brah, L. Vandendorpe, On the Lambert-W function for CDIT-based power allocation in cooperative relay networks, 5th International Symposium on Wireless Pervasive Computing (ISWPC) (2010), 11-15.
T. Cui, T. Ho, J. Kliewer, Memoryless Relay Strategies for Two-Way Relay Channels: Performance Analysis and Optimization , IEEE International Conference on Communications proceedings (2008), 1139-1143.
2.f Biology, Chemistry
Z. Gromotka, G. Yablonsky, N. Ostrovskii, D. Constales, Integral characteristic of complex catalytic reaction accompanied by deactivation, Catalysts 12 (2022), 1283. pdf
D. Belkić, All the trinomial roots, their powers and logarithms from the Lambert series, Bell polynomials and Fox–Wright function: illustration for genome multiplicity in survival of irradiated cells, J. Math. Chemistry 57 (2019), 59-106. pdf
M. Goličnik, On the Lambert W function and its utility in biochemical kinetics, Biochem. Eng. J. 63 (2012), 116–123.
Ch. T. Goudar, An explicit solution for progress curve analysis in systems characterized by endogenous substrate production, Microbial Ecology 63 (2012), 898-904.
B. W. Williams, The utility of the Lambert function W[a exp(a−bt)] in chemical kinetics, J. Chem. Educ. 87 (2010) 647–651.
2.g Sociology
R. Wallace, Evolutionary exaptation: shared interbrain activity in social communication, Essays on the Extended Evolutionary Synthesis, Springer, 2023. (link to the publisher's webpage)
R. Wallace, Punctuated Institutional Problem Recognition, in Essays on Strategy and Public Health, Springer, 2022.
R. Wallace, Formal perspectives on shared interbrain activity in social communication, Cognitive Neurodynamics (2022), DOI: 10.1007/s11571-022-09811-4
R. Wallace, ``Neuroscience'' models of institutional conflict under fog, friction, and adversarial intent, The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology (online first)
S. Bhamidi, J. M. Steele, T. Zaman, Twitter event networks and the Superstar model, Ann. Appl. Probab. 25(5) (2015), 2462-2502.
3. Generalizations and analogues of the Lambert W function
3.a Matrix Lambert function
R. Cepeda-Gomez, W. Michiels, Special Cases in Using the Matrix Lambert W function for the Stability Analysis of High-Order Linear Systems with Time Delay, IFAC-PapersOnLine, 48(12) (2015), 7-12. pdf
M. Fasi, N. J. Higham and B. Iannazzo, An algorithm for the matrix Lambert W function, MIMS Eprint 2014.58 (2014). pdf See this link for an algorithm for the matrix Lambert W function.
K.M. Pietarila, Developing and automating time delay system stability analysis of dynamic systems using the matrix Lambert function W (MLF) method. PhD thesis, University of Missouri, 2008.
R. M. Corless, H. Ding, N. J. Higham, D. J. Jeffrey, The solution of S*exp(S)=A is not always the Lambert W function of A, ISSAC '07, 116-121. pdf
3.b Discrete Lambert map
J. Holden, P. A. Richardson, M. M. Robinson, Counting fixed points and two-cycles of the singular map x ↦ x^(x^n), Mathematical Sciences Technical Reports 16-5, 2016. pdf at ArXiv
M. K. Mahmood, L. Anwar, Loops in digraphs of Lambert mapping modulo prime powers: enumerations and applications, Adv. Pure Math. 6 (2016), 564-570. pdf
C.-Y. Zhu, A. Waldo, The discrete Lambert map, Rose-Hulman Undergraduate Mathematics Journal 16(2) (2015), 180-194. view content
D. Zirlin, Problems motivated by cryptology: counting fixed points and two-cycles of the discrete Lambert map, thesis presented at Mount Holyoke college, 2015. pdf
J.-J. Chen, M. Lotts, Structure and randomness of the discrete Lambert map, Rose-Hulman Undergraduate Mathematics Journal 13(1) (2012), 62-99. view content
3.c Generalized Lambert function, r-Lambert function, quadratic Lambert function
Theory
C. B. Corcino, R. B. Corcino, I. Mező, Integrals and derivatives connected to the r-Lambert function, Int. Trans. Spec. Funct. 28(11) (2017), 838-845.
I. Mező, On the structure of the solution set of a generalized Euler–Lambert equation, J. Math. Anal. Appl. 455 (2017) 538–553.
I. Mező, Á. Baricz, On the generalization of the Lambert W function, Trans. Amer. Math. Soc. 369(11) (2017), 7917-7934.
Applications
J. L. Rocha, A.-K. Taha Bifurcation structures of the homographic \gamma-Ricker maps and their cusp points organization, Int. J. Bifurcation and Chaos 33(5) (2023), 2330011
J. L. Rocha, A.-K. Taha, Generalized Lambert functions in gamma-Ricker population models with a Holling type II per-capita birth function, Commun. Nonlin. Sci. Numer. Simul. 120 (2023), 107187
M. Kozlov, A. Tulendinova, J. Kim, G. Ellis, P. Skrzypacz, Oscillations of retaining wall subject to Grob’s swelling pressure, Nature Scientific Reports 12 (2022), Article no. 12224. pdf
D. A. Gomez, D. Frydel, Y. Levin, Lattice-gas model of a charge regulated planar surface, J. Chemical Phys. 154(7) (2021), 074706 full text online
J. L. Rocha, A.-K. Taha, Generalized r-Lambert function in the analysis of fixed points and bifurcations of homographic 2-Ricker maps, Int. J. Bifurcation and Chaos 31(11) (2021), Article no: 2130033.
C. Jamilla, R. Mendoza, I. Mező, Solutions of neutral delay differential equations using a generalized Lambert W function, Appl. Math. Comp. 382 (2020).
C. Jamilla, R. G. Mendoza, V. M. P. Mendoza, Explicit solution of a Lotka-Sharpe-McKendrick system involving neutral delay differential equations using the r-Lambert W function, Mathematical Biosciences and Engineering 17(5) (2020), 5686-5708. link to pdf
T. Gemechu, S. Thota, On new root finding algorithms for solving nonlinear transcendental equations, International journal of Chemistry, Mathematics and Physics, 4(2) (2020), 18-24. pdf
I. Mező, C. B. Corcino, R. B. Corcino, Resolution of the Plane-symmetric Einstein-Maxwell fields with a generalization of the Lambert W function, J. Phys. Commun. 4 (2020), 085008. (quadratic Lambert)
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