Computation of certain infinite series of the form Sigma f(n)nk for arbitrary real-valued k

We provide a general method from which one may obtain more arbitrary closed form solutions for infinite series of the form @?f(n)n^k, for [email protected]?R and sufficiently well-behaved f(n). We illustrate the methods for the special case of f(n)=a^n/n!, obtaining generalizations to the Bell numbers and polynomials.

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