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Stirling Polynomials in Several Indeterminates free ebook download

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Mathematics

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Author(s):	Alfred Schreiber

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3832552502
Pages:	160	OCR:		Quality:		ISBN13:	9783832552503
Uploader:	tvladb77	Upload Date:	1/11/2023 9:32:54 PM

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The classical exponential polynomials, today commonly named after E., T. Bell, have a wide range of remarkable applications in Combinatorics, Algebra, Analysis, and Mathematical Physics. Within the algebraic framework presented in this book they appear as structural coefficients in finite expansions of certain higher-order derivative operators. In this way, a correspondence between polynomials and functions is established, which leads (via compositional inversion) to the specification and the effective computation of orthogonal companions of the Bell polynomials. Together with the latter, one obtains the larger class of multivariate 'Stirling polynomials'. Their fundamental recurrences and inverse relations are examined in detail and shown to be directly related to corresponding identities for the Stirling numbers. The following topics are also covered: polynomial families that can be represented by Bell polynomials  inversion formulas, in particular of Schlomilch-Schlafli type  applications to binomial sequences  new aspects of the Lagrange inversion, and, as a highlight, reciprocity laws, which unite a polynomial family and that of orthogonal companions. Besides a Mathematica(R) package and an extensive bibliography, additional material is compiled in a number of notes and supplements.

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Tags: Indeterminates Polynomials Several Stirling

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Stirling Polynomials in Several Indeterminates free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics