# Tag Info

Recall that $(-n)_k=0$ for $k>n, n,k\in\mathbb N$. Thus, what you have is an appropriate truncation of the usual series for the Kummer function. With[{a = 9}, Sum[Pochhammer[1/2 - a/2, k] (-x)^k/(Pochhammer[3/2, k] k!), {k, 0, a/2 - 1/2}]] 1 + (8 x)/3 + (8 x^2)/5 + (32 x^3)/105 + (16 x^4)/945