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In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling polynomial sequence considered below most notably including the Sheffer sequence form of the sequence, , defined characteristically through the special form of its exponential generating function, and the Stirling (convolution) polynomials, , which also satisfy a characteristic ordinary generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "convolution polynomial" variant of this sequence

Attributes	Values
rdfs:label	Stirling polynomials (en)
rdfs:comment	In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling polynomial sequence considered below most notably including the Sheffer sequence form of the sequence, , defined characteristically through the special form of its exponential generating function, and the Stirling (convolution) polynomials, , which also satisfy a characteristic ordinary generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "convolution polynomial" variant of this sequence (en)
dcterms:subject	Polynomials
Wikipage page ID	4069580 (xsd:integer)
Wikipage revision ID	1105501760 (xsd:integer)
Link from a Wikipage to another Wikipage	Bernoulli number Bernoulli numbers Bernoulli polynomials Appell sequence Complex number Analysis Mathematics Generating function Generating functions Bernoulli polynomials of the second kind Combinatorics Stirling number Difference polynomials Gregory coefficients Polynomials Laguerre polynomials Binomial type Double factorial Polynomial Integer Sheffer sequence Stirling numbers of the second kind Stirling numbers of the first kind Stirling polynomial Lagrange interpolation Bernoulli polynomial Stirling number of the first kind Stirling numbers dbr:Generalized_Bernoulli_polynomials dbr:Nørlund_polynomials
sameAs	Stirling polynomials Stirling polynomials Stirling polynomials Stirling polynomials
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:MathWorld dbt:More_footnotes dbt:Reflist dbt:PlanetMath_attribution
id	37575 (xsd:integer)
title	Stirling polynomial (en) Nørlund Polynomial (en) Stirling Polynomial (en)
urlname	NorlundPolynomial (en) StirlingPolynomial (en)
has abstract	In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling polynomial sequence considered below most notably including the Sheffer sequence form of the sequence, , defined characteristically through the special form of its exponential generating function, and the Stirling (convolution) polynomials, , which also satisfy a characteristic ordinary generating function and that are of use in generalizing the Stirling numbers (of both kinds) to arbitrary complex-valued inputs. We consider the "convolution polynomial" variant of this sequence and its properties second in the last subsection of the article. Still other variants of the Stirling polynomials are studied in the supplementary links to the articles given in the references. (en)
gold:hypernym	Family
prov:wasDerivedFrom	wikipedia-en:Stirling_polynomials?oldid=1105501760&ns=0
page length (characters) of wiki page	13232 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stirling_polynomials
is Link from a Wikipage to another Wikipage of	James Stirling (mathematician) Bernoulli polynomials of the second kind Gregory coefficients Mittag-Leffler polynomials Pochhammer k-symbol Poly-Bernoulli number Stirling numbers of the second kind Stirling numbers of the first kind Stirling polynomial
is Wikipage redirect of	Stirling polynomial
is foaf:primaryTopic of	wikipedia-en:Stirling_polynomials

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