Laurent series

In mathematics, the Laurent series of a complex function $f(z)$ is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass had previously described it in a paper written in 1841 but not published until 1894.^[1]

^ Roy, Ranjan (2012), "§1.5 Appendix: Historical Notes by Ranjan Roy", Complex Analysis: In the Spirit of Lipman Bers, by Rodríguez, Rubí E.; Kra, Irwin; Gilman, Jane P. (2nd ed.), Springer, p. 12, doi:10.1007/978-1-4419-7323-8_1, ISBN 978-1-4419-7322-1

Weierstrass, Karl (1841), "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt" [Representation of an analytical function of a complex variable, whose absolute value lies between two given limits], Mathematische Werke (in German), vol. 1, Berlin: Mayer & Müller (published 1894), pp. 51–66

[1] Roy, Ranjan (2012), "§1.5 Appendix: Historical Notes by Ranjan Roy", Complex Analysis: In the Spirit of Lipman Bers, by Rodríguez, Rubí E.; Kra, Irwin; Gilman, Jane P. (2nd ed.), Springer, p. 12, doi:10.1007/978-1-4419-7323-8_1, ISBN 978-1-4419-7322-1

Weierstrass, Karl (1841), "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt" [Representation of an analytical function of a complex variable, whose absolute value lies between two given limits], Mathematische Werke (in German), vol. 1, Berlin: Mayer & Müller (published 1894), pp. 51–66

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