A new nonelementary real-valued function of the Dawson’s integral type is studied. It is constructed as a power series with the help of rising factorial powers. Its connection with the error function is determined. It is proved that the new function is a solution of the Riccati equation.
rising factorial power, Dawson’s integral, error function, Riccati equation.
Introduction. Duality of rising and falling factorial powers is a common feature in the combinatorial analysis. In other words, if a problem leads to some combinatorial identity constructed with the help of falling factorial powers, then often there is a dual combinatorial problem, which leads to a dual combinatorial identity involving rising factorial powers. One can find some examples of these dual combinatorial identities in [1-3].
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