New integral functions generated by rising factorial powers

T. P. Goy, R. A. Zatorsky

Abstract


We consider new nonelementary functions such as the Fresnel integrals, generated by rising factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is shown, that new integral functions are solutions of second order ordinary differential equations with variable coefficients.

Keywords


factorial power, rising factorial power, Fresnel integrals, power series, Cauchy problem

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