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Quintic function
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==References== * Charles Hermite, "Sur la résolution de l'équation du cinquème degré", ''Œuvres de Charles Hermite'', '''2''':5–21, Gauthier-Villars, 1908. * {{cite book |first=Felix |last=Klein |url=https://archive.org/details/cu31924059413439 |title=Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree |translator-first=George Gavin |translator-last=Morrice |publisher=Trübner & Co. |date=1888 |isbn=0-486-49528-0}} * Leopold Kronecker, "Sur la résolution de l'equation du cinquième degré, extrait d'une lettre adressée à M. Hermite", ''Comptes Rendus de l'Académie des Sciences'', '''46''':1:1150–1152 1858. * Blair Spearman and Kenneth S. Williams, "Characterization of solvable quintics {{math|''x''<sup>5</sup> + ''ax'' + ''b''}}, ''American Mathematical Monthly'', '''101''':986–992 (1994). * Ian Stewart, ''Galois Theory'' 2nd Edition, Chapman and Hall, 1989. {{isbn|0-412-34550-1}}. Discusses Galois Theory in general including a proof of insolvability of the general quintic. * [[Jörg Bewersdorff]], ''Galois theory for beginners: A historical perspective'', American Mathematical Society, 2006. {{isbn|0-8218-3817-2}}. Chapter 8 ({{webarchive|url=https://web.archive.org/web/20100331181637/http://www.ams.org/bookstore/pspdf/stml-35-prev.pdf|title=The solution of equations of the fifth degree|date=31 March 2010}}) gives a description of the solution of solvable quintics {{math|''x''<sup>5</sup> + ''cx'' + ''d''}}. * Victor S. Adamchik and David J. Jeffrey, "Polynomial transformations of Tschirnhaus, Bring and Jerrard," ''ACM SIGSAM Bulletin'', Vol. 37, No. 3, September 2003, pp. 90–94. * Ehrenfried Walter von Tschirnhaus, "A method for removing all intermediate terms from a given equation," ''ACM SIGSAM Bulletin'', Vol. 37, No. 1, March 2003, pp. 1–3. * {{Cite book | last1 = Lazard | first1 = Daniel | chapter = Solving quintics in radicals | title = The Legacy of Niels Henrik Abel | editor1 = [[Olav Arnfinn Laudal]] | editor2 = [[Ragni Piene]] | location = Berlin | pages = 207–225 | year = 2004 | isbn = 3-540-43826-2 | url = https://www.loria.fr/publications/2002/A02-R-449/A02-R-449.ps | archive-url = https://web.archive.org/web/20050106213419/http://www.loria.fr/publications/2002/A02-R-449/A02-R-449.ps | archive-date=January 6, 2005 }} * {{citation | title = Finite Möbius groups, minimal immersions of spheres, and moduli| first = Gábor | last = Tóth | year = 2002 }}
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