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In [[mathematics]], the '''Humbert polynomials''' π{{su|b=''n'',''m''|p=λ}}(''x'') are a generalization of [[Pincherle polynomials]] introduced by {{harvs|txt|last=Humbert|year=1921|authorlink=Pierre Humbert (mathematician)}} given by the [[generating function]]


:<math>\displaystyle (1-mxt+t^m)^{-\lambda}=\sum^\infty
_{n=0}\pi^\lambda_{n,m}(x)t^n</math>


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{{harvtxt|Boas|Buck|1958|loc=p.58}}.


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==See also==


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*[[Umbral calculus]]


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==References==


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*{{Citation | last1=Boas | first1=Ralph P. | last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=http://books.google.com/books?id=eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 | year=1958 | volume=19}}
*{{Citation | last1=Humbert | first1=Pierre | title=Some extensions of Pincherle's Polynomials | doi=10.1017/S0013091500035756 | year=1921 | journal=Proceedings of the Edinburgh mathematics society | volume=39 | pages=21–24}}


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[[Category:Polynomials]]

Revision as of 17:33, 16 May 2013

In mathematics, the Humbert polynomials πTemplate:Su(x) are a generalization of Pincherle polynomials introduced by Template:Harvs given by the generating function

(1mxt+tm)λ=n=0πn,mλ(x)tn

Template:Harvtxt.

See also

References

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