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# Tag Archives: Falling factorial

## Goin’ with the Flow: Logarithm of the Derivative

Goin’ with the Flow: Logarithm of the Derivative Operator is a pdf set of notes under construction on the relations between the commutator of the logarithm of the derivative operator, the Pincherle derivative, Lie operator derivatives, and the two umbrally inverse … Continue reading

Posted in Math
Tagged Bell polynomials, Binomial Sheffer sequences, Commutatator, Confluent hypergeometric functions, Differential operators, Factorial polynomials, Falling factorial, Flow equations, Fractional calculus, Generalized Laguerre functions, Inversion, Laguerre polynomials, Lie derivatives, Logarithm of the derivative operator, Matrix representations, Operator calculus, Pincherle derivative, Rising factorial, Sheffer sequences, Simplices, Stirling numbers, Vandermonde matrix
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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

Posted in Math
Tagged Bell polynomials, Cayley trees, Composition, Compositional inverse, Differential operators, Faa di Bruno formula, Falling factorial, Forests, Generalized shift operator, Generlized Taylor series, Lagrange inversion, Lagrange partition polynomials, Lah polynomials, Operator calculus, Partition polynomials, Rising factorial, Sheffer sequences, Special functions, Special polynomials, Stirling numbers, Stirling polynomials, Tree graphs, Trees, Umbral calculus, Umbral operator trees
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