Stirling polynomials

rdf:langString Stirling polynomials

rdf:langString Stirling polynomial

rdf:langString Nørlund Polynomial

rdf:langString Stirling Polynomial

rdf:langString NorlundPolynomial

rdf:langString StirlingPolynomial

rdf:langString 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.