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# Tag Archives: Generalized Dobinski relation

## 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

Posted in Math
Tagged Associahedra, Bell polynomials, Differential operators, Falling factorials, Generalized Dobinski relation, Generalized Stirling numbers, Lah polynomials, Lie derivatives, Moebius transformation, Rising factorials, SL2 group, Stirling numbers of the first kind, Stirling numbers of the second kind, Umbral calculus, Umbral inverse pair, Witt-Lie algebra
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## Differential Ops, Special Polynomials, Binomial Transforms, Interpolation, and the Inverse Mellin Transform

Differential Ops, Special Polynomials, Binomial Transforms, Interpolation, and the Inverse Mellin Transform: (pdf, under construction. ) Relations between differential operators represented in the two basis sets and and the underlying binomial transforms of the associated coefficients of the pairs of … Continue reading

Posted in Math
Tagged Associated Laguerre polynomials, Bell polynomials, Binomial transform, Differential operators, Euler transformations, Falling factorials, Finite differences, Generalized Dobinski relation, Inverse Mellin transform, Mellin transform, Modular forms and eigenfunctions, Newton interpolation, Number operator, Permutahedra face polynomials, Stirling numbers of the second kind, Touchard polynomials, Umbral composition
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## A Generalized Dobinski Relation and the Confluent Hypergeometric Fcts.

The Inverse Mellin Transform, Bell Polynomials, a Generalized Dobinski Relation, and the Confluent Hypergeometric Functions presents a generalized Dobinski relation umbrally incorporating the Bell / Touchard / Exponential polynomials that is defined operationally through the action of the operator f(x d/dx) … Continue reading