In mathematics, the Faber polynomials Pm of a Laurent series

are the polynomials such that

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

References

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  • Curtiss, J. H. (1971), "Faber Polynomials and the Faber Series", The American Mathematical Monthly, 78 (6), Mathematical Association of America: 577–596, doi:10.2307/2316567, ISSN 0002-9890, JSTOR 2316567
  • Faber, Georg (1903), "Über polynomische Entwickelungen" (PDF), Mathematische Annalen, 57, Springer Berlin / Heidelberg: 389–408, doi:10.1007/BF01444293, ISSN 0025-5831
  • Faber, G. (1919), "Über Tschebyscheffsche Polynome.", Journal für die reine und angewandte Mathematik (in German), 150: 79–106, ISSN 0075-4102, JFM 47.0315.01
  • 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, JSTOR 2371913, MR 0011740
  • Suetin, P. K. (1998) [1984], Series of Faber polynomials, Analytical Methods and Special Functions, vol. 1, New York: Gordon and Breach Science Publishers, ISBN 978-90-5699-058-9, MR 1676281
  • Suetin, P. K. (2001) [1994], "Faber polynomials", Encyclopedia of Mathematics, EMS Press