Is the generalized hypergeometric function ${}_1F_2\bigl(1;a,a+\frac12;x\bigr)$${}_1F_2\bigl(1;a,a+\frac12;-x^2\bigr)$ for $a>2$$a>-1$ and $x<0$$x>0$ an elementary function?
How about the positivity, monotonicity, and convexity of the generalized hypergeometric function ${}_1F_2\bigl(1; a, a+\frac{1}{2}; -x^2\bigr)$ in $x>0$ for $a\ge-1$?