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.
- Infinigens, the Pascal Triangle, and the Witt and Virasoro Algebras
- Depressed Equations and Generalized Catalan Numbers
- Riemann’s Jump Function J(x) for the Primes
- A Generalized Dobinski Relation and the Confluent Hypergeometric Fcts.
- Note on the Inverse Mellin Transform and the Dirac Delta Function.