Faber polynomials

In mathematics, the Faber polynomials Pm of a Laurent series

f(z)=z−1+a0+a1z+⋯

are the polynomials such that

Pm(f)−z−m

vanishes at z=0. They were introduced by Faber (1903, 1919) and studied by Grunsky (1939) and Schur (1945).

## References

* Curtiss, J. H. (1971), "Faber Polynomials and the Faber Series", The American Mathematical Monthly (Mathematical Association of America) 78 (6): 577–596, doi:10.2307/2316567, ISSN 0002-9890
* Faber, Georg (1903), "Über polynomische Entwickelungen", Mathematische Annalen (Springer Berlin / Heidelberg) 57: 389–408, doi:10.1007/BF01444293, ISSN 0025-5831, https://zenodo.org/record/2129496/files/article.pdf
* Faber, G. (1919), "Über Tschebyscheffsche Polynome." (in German), Journal für die reine und angewandte Mathematik 150: 79–106, ISSN 0075-4102, http://resolver.sub.uni-goettingen.de/purl?GDZPPN00216874X
* Grunsky, Helmut (1939), "Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen", Mathematische Zeitschrift 45 (1): 29–61, doi:10.1007/BF01580272, ISSN 0025-5874
* Schur, Issai (1945), "On Faber polynomials", American Journal of Mathematics 67: 33–41, doi:10.2307/2371913, ISSN 0002-9327
* Suetin, P. K. (1998) [1984], Series of Faber polynomials, Analytical Methods and Special Functions, 1, New York: Gordon and Breach Science Publishers, ISBN 978-90-5699-058-9, https://books.google.com/books?id=uZZS0Eeh5RMC
* Hazewinkel, Michiel, ed. (2001), "Faber polynomials", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Main_Page

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