ランベルトのW関数
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2023/12/31 03:36 UTC 版)
ランベルトのW函数（ランベルトのWかんすう、英: Lambert W function）あるいはオメガ函数 (ω function)、対数積（product logarithm; 乗積対数）は、函数 f(z) = zez の逆関係の分枝として得られる函数 W の総称である。ここで、ez は指数函数、z は任意の複素数とする。すなわち、W は z = f−1(zez) = W(zez) を満たす。
- ^ Chow, Timothy Y. (1999), “What is a closed-form number?”, American Mathematical Monthly 106 (5): 440–448, doi:10.2307/2589148, MR1699262.
- ^ a b Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jeffrey, D. J.; Knuth, D. E. (1996). “On the Lambert W function” (PostScript). Advances in Computational Mathematics 5: 329–359. doi:10.1007/BF02124750.
- ^ Lambert JH, "Observationes variae in mathesin puram", Acta Helveticae physico-mathematico-anatomico-botanico-medica, Band III, 128–168, 1758 (facsimile)
- ^ Euler, L. "De serie Lambertina Plurimisque eius insignibus proprietatibus." Acta Acad. Scient. Petropol. 2, 29–51, 1783. Reprinted in Euler, L. Opera Omnia, Series Prima, Vol. 6: Commentationes Algebraicae. Leipzig, Germany: Teubner, pp. 350–369, 1921. (facsimile)
- ^ Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jeffrey, D. J. (1993). “Lambert's W function in Maple”. The Maple Technical Newsletter (MapleTech) 9: 12–22. CiteSeerx: 10.1.1.33.2556.
- ^ Approximation of the Lambert W function and the hyperpower function, Hoorfar, Abdolhossein; Hassani, Mehdi.
- ^ http://www.emis.de/journals/JIPAM/images/107_07_JIPAM/107_07_www.pdf
- ^ Chatzigeorgiou, I. (2013). “Bounds on the Lambert function and their Application to the Outage Analysis of User Cooperation” (PDF). IEEE Communications Letters 17 (8): 1505–1508. doi:10.1109/LCOMM.2013.070113.130972.
- ^ Weisstein, Eric W. "Lambert W-Function". mathworld.wolfram.com (英語).
- ^ The Lambert W Function, Ontario Research Centre
- ^ Scott, T. C.; Mann, R. B.; Martinez Ii, Roberto E. (2006). “General Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function”. AAECC (Applicable Algebra in Engineering, Communication and Computing) 17 (1): 41–47. arXiv:math-ph/0607011. doi:10.1007/s00200-006-0196-1.
- ^ Scott, T. C.; Fee, G.; Grotendorst, J. (2013). “Asymptotic series of Generalized Lambert W Function”. SIGSAM (ACM Special Interest Group in Symbolic and Algebraic Manipulation) 47 (185): 75–83. doi:10.1145/2576802.2576804.
- ^ Scott, T. C.; Fee, G.; Grotendorst, J.; Zhang, W.Z. (2014). “Numerics of the Generalized Lambert W Function”. SIGSAM 48 (188): 42–56. doi:10.1145/2644288.2644298.
- ^ Maignan, Aude; Scott, T. C. (2016). “Fleshing out the Generalized Lambert W Function”. SIGSAM 50 (2): 45–60. doi:10.1145/2992274.2992275.
- ^ Farrugia, P. S.; Mann, R. B.; Scott, T. C. (2007). “N-body Gravity and the Schrödinger Equation”. Class. Quantum Grav. 24 (18): 4647–4659. arXiv:gr-qc/0611144. doi:10.1088/0264-9381/24/18/006.
- ^ Scott, T. C.; Aubert-Frécon, M.; Grotendorst, J. (2006). “New Approach for the Electronic Energies of the Hydrogen Molecular Ion”. Chem. Phys. 324 (2–3): 323–338. arXiv:physics/0607081. doi:10.1016/j.chemphys.2005.10.031.
- ^ Scott, T. C.; Lüchow, A.; Bressanini, D.; Morgan, J. D. III (2007). “The Nodal Surfaces of Helium Atom Eigenfunctions”. Phys. Rev. A 75 (6): 060101. doi:10.1103/PhysRevA.75.060101.
- ^ McPhedran, R. C.; Scott, T.C.; Maignan, Aude (2023). “The Keiper-Li Criterion for the Riemann Hypothesis and Generalized Lambert Functions”. ACM Commun. Comput. Algebra 57 (3): 85-110. doi:10.1145/3637529.3637530.
- ^ lambertw - MATLAB
- ^ Maxima, a Computer Algebra System
- ^ ProductLog at WolframAlpha
- ^ [1]
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