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Differintegral methods, currently exploited in calculus, provide a fairlyunexhausted source of tools to be applied to a wide class of problems involvingthe theory of special functions and not only. The use of integral transforms ofBorel type and the associated formalism will be shown to be an effective means,allowing a link between umbral and operational methods. We merge these twopoints of view to get a new and efficient method to obtain integrals of specialfunctions and the summation of the associated generating functions as well.

Operational vs. Umbral Methods and Borel Transform