Tag Archives: Stirling polynomials of the second kind
Composition, Conjugation, and the Umbral Calculus–Part I
Relationships among a set of Appell and binomial Sheffer sequences derived from the function , its compositional inverse, and their multiplicative inverses are re-explored in the pdf below, and a simple formula for calculating the Bernoulli numbers from the Stirling … Continue reading
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Tagged Abel polynomials, Appell matrices, Appell sequences, Bell polynomials, Bernoulli polynomials, Compositional inverse, Falling factorials, Functional composition, Functional iteration, Hyperbinomial polynomials, Lambert W-function, Matrix cojugation, Multiplicative inverse, Pascal matrix, Reciprocal polynomials, Sheffer matrices, Sheffer polynomials, Stirling polynomials of the first kind, Stirling polynomials of the second kind, Umbral calculus, umbral compositional inverse, Umbral conjugation
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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
Posted in Math
Tagged Bell polynomials, Confluent hypergeometric functions, Differential operators, Dirac delta function, Euler operator, Fractional calculus, Generalized Dobinski relation, Generalized Laguerre polynomials / functions, Inverse Mellin transform, Kummer, Mellin transform interpolation, Operator calculus, Ramanujan Master Formula / Theorem, Stirling polynomials of the second kind, Tricomi
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Shadows of Simplicity 