View source for Narumi polynomials

{{format footnotes |date=May 2024}}
In mathematics, the '''Narumi polynomials''' ''s''<sub>''n''</sub>(''x'') are polynomials introduced by {{harvtxt|Narumi|1929}} given by the [[generating function]]

:<math>\displaystyle \sum s_n(x)t^n/n! = \left(\frac{t}{\log(1+t)}\right)^a(1+t)^x</math>

{{harv|Roman|1984|loc=4.4}}, {{harv|Boas|Buck|1958|loc=p.37}}

==See also==
*[[Umbral calculus]]

==References==

*{{Citation | last1=Boas | first1=Ralph P. | last2=Buck | first2=R. Creighton | title=Polynomial expansions of analytic functions | url=https://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| isbn=9783540031239 }}
*{{Citation | last1=Narumi | first1=S. | title=On a power series having only a finite number of algebraico logarithmic singularities on its circle of convergence. | url=http://www.journalarchive.jst.go.jp/english/jnlabstract_en.php?cdjournal=tmj1911&cdvol=30&noissue=0&startpage=185 | jfm=55.0185.03 | year=1929 | journal=[[Tohoku Mathematical Journal]] | volume=30 | pages=185–201}}
*{{Citation | last1=Roman | first1=Steven | title=The umbral calculus | url=https://books.google.com/books?id=JpHjkhFLfpgC | publisher=Academic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=1984 | volume=111}} Reprinted by Dover, 2005

[[Category:Polynomials]]


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