# Tag Archives: Rising factorials

## Fractional Calculus, Gamma Classes, the Riemann Zeta Function, and an Appell Pair of Sequences

The background info and comments for the MSE question Lie group heuristics for a raising operator for and the MO question Riemann zeta function at positive integers and an Appell sequence of poylnomials introduce an Appell sequence of polynomials containing … Continue reading

Posted in Math
Tagged Appell sequences, Associated Laguerre polynomials, Bell polynomials, Confluent hypergeometric functions, Convolution operators, Creation and annihilation operators, Cycle index polynomials, Differential operators, Digamma function, Falling factorials, Fractional calculus, Gamma classes, Gamma genus, Infinitesimal generators, Inverse Mellin transform, Mellin transform, Psi function, Raising and lowering operators, Riemann zeta function, Rising factorials, Umbral calculus, Umbral compositional inverse pair
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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

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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