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) on a modified inverse Mellin transform. Relations to the Dirac delta function/operator and, through an appropriate choice of f, the confluent hypergeometric functions, one set of which are the generalized Laguerre functions, are sketched and finally some exercises presented.

The exercises include formulas for the Riemann-Liouville and Weyl fractional integroderivatives (differintegrals) and their relations to an umbral Euler integral for the gamma function and the Kummer and Tricomi confluent hypergeometric functions.

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