View source for Share of the audience

In mathematics, the '''Faber polynomials''' ''P''<sub>''m''</sub> of a [[Laurent series]]
:<math>\displaystyle f(z)=z^{-1}+a_0+a_1z+\cdots</math>
are the polynomials such that
:<math>\displaystyle P_m(f)-z^{-m}</math>
vanishes at ''z''=0. They were introduced by {{harvs |txt |last=Faber |authorlink=Georg Faber |year1=1903 |year2=1919}} and studied by {{harvs|txt|last=Grunsky|authorlink=Helmut Grunsky|year=1939}} and {{harvs|txt|last=Schur|authorlink=Issai Schur|year=1945}}.

==References==

*{{Citation | last1=Curtiss | first1=J. H. | title=Faber Polynomials and the Faber Series | jstor=2316567 | publisher=[[Mathematical Association of America]] | year=1971 | journal=[[American Mathematical Monthly|The American Mathematical Monthly]] | issn=0002-9890 | volume=78 | issue=6 | pages= 577–596}}
*{{Citation | last1=Faber | first1=Georg | title=Über polynomische Entwickelungen | doi=10.1007/BF01444293 | publisher=Springer Berlin / Heidelberg | year=1903 | journal=[[Mathematische Annalen]] | issn=0025-5831 | volume=57 | pages=389–408}}
*{{Citation | last1=Faber | first1=G. | title=Über Tschebyscheffsche Polynome. | url=http://resolver.sub.uni-goettingen.de/purl?GDZPPN00216874X | language=German | jfm=47.0315.01 | year=1919 | journal=[[Journal für die reine und angewandte Mathematik]] | issn=0075-4102 | volume=150 | pages=79–106}}
*{{Citation | last1=Grunsky | first1=Helmut | title=Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen | doi=10.1007/BF01580272 | year=1939 | journal=[[Mathematische Zeitschrift]] | issn=0025-5874 | volume=45 | issue=1 | pages=29–61}}
*{{Citation | last1=Schur | first1=Issai | title=On Faber polynomials | jstor=2371913 | mr=0011740 | year=1945 | journal=[[American Journal of Mathematics]] | issn=0002-9327 | volume=67 | pages=33–41}}
*{{Citation | last1=Suetin | first1=P. K. | title=Series of Faber polynomials | origyear=1984 | url=http://books.google.com/books?id=uZZS0Eeh5RMC | publisher=Gordon and Breach Science Publishers | location=New York | series=Analytical Methods and Special Functions | isbn=978-90-5699-058-9 | mr=1676281 | year=1998 | volume=1}}
*{{eom|id=f/f038010|first=P. K.|last= Suetin}}

[[Category:Polynomials]]