Abstract
We study two new real-valued non-elementary functions generated by central factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is also shown that new integral functions are solutions of fourth order linear ordinary differential equations with variable coefficients.
Highlights
Mathematical models of many natural processes and phenomena lead to problems, exact solutions of which can not be obtained by well-known classical methods
+ + k is called the central factorial power m with the step k > 0
Central factorial powers with the step 1 we will denote by x[m]
Summary
Mathematical models of many natural processes and phenomena lead to problems, exact solutions of which can not be obtained by well-known classical methods. In [6] we defined new non-elementary functions Sinc x, Cosc x constructed by replacing in a power series of trigonometric functions sin x, cos x falling factorial powers nn (i.e. usual factorials) by corresponding central powers n[n]. In [8] we studied similar functions constructed using rising factorial powers. Factorial power xm{k} is called rising if k > 0 and is called falling if k < 0.
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