Using a power series to solve an ordinary differential equation will often result in a solution whose general term involves a product of terms from an arithmetic sequence. This paper explores how factorials and the gamma function can be used to rewrite such general terms in a closed form.
Ordinary Differential Equations and Applied Dynamics
Wilson, Steven J., "Series Solutions, Factorials, And The Gamma Function" (1994). Topics in Mathematics. 1.
This paper was originally prepared for student use in a beginning class in Ordinary Differential Equations.