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A Symbolic Treatment of Abel Polynomials

Contributed Chapter
  • Pasquale Petrullo

Abstract

We study the umbral polynomials A(k) n(x, α) = x(xk·α) n−1, by means of which a wide range of formal power series identities, including Lagrange inversion formula, can be usefully manipulated. We apply this syntax within cumulant theory, and show how moments and its formal cumulants (classical, free and Boolean) are represented by polynomials A(k) n(α, γ) for suitable choices of umbrae α and γ.

Keywords

Formal Power Series Noncrossing Partition Parking Function Free Convolution Free Probability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Pasquale Petrullo
    • 1
  1. 1.Università degli Studi della BasilicataBasilicataItaly

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