Tag Archives: Lah polynomials

Generators, Inversion, and Matrix, Binomial, and Integral Transforms

Generators, Inversion, and Matrix, Binomial, and Integral Transforms is a belated set of notes (pdf) on a derivation of a generating function for the row polynomials of  OEIS-A111999 from its relation to the compositional inversion (a Lagrange inversion formula, LIF) presented … Continue reading

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A Class of Differential Operators and the Stirling Numbers

The differential operator with can easily be expanded in terms of the operators by considering its action on

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Bernoulli Appells

The defining characteristic of the Bernoulli numbers operationally is that they are the basis of the unique Appell sequence, the Bernoulli polynomials, that “translate” simply under the generalized binomial transform (Appell property) and satisfy (for an analytic function, such as … Continue reading

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Lagrange à la Lah

 Lagrange à la Lah Part I and Lagrange à la Lah Part II are a set of notes on partition polynomials derived from binomial Sheffer sequences via umbral refinement, their relation to compositional inversion via the Laplace transform, and their characterization by umbral … Continue reading

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