I want to see if I can find a closed form expression for the following $$_3F_2\left(a,b,-\frac{1}{2};a-\frac{1}{2},a+b;1\right)=\sum_{l\ge 0}\frac{(-1/2)_l(a)_l(b)_l}{(a-1/2)_l(a+b)_l}\frac{1}{l!},$$ where $a,b>0$. The Pochhammer symbol $(a)_l$ is defined as $(a)_l=a(a+1\cdots (a+l-1)$, for $l\ge 1$ and $(a)_0=1$.
Although I found plenty of identities involving $_3F_2$ after a search, for example Watson's identity, Whipple's identity and so on, I could not find one of the above form.
I am also not sure how to proceed simplifying this expression. I tried writing it down and finding some simplifications, but could not find any obvious simplification. Maybe there are some specific techniques for finding a simplification to this kind of expressions. Can someone find a concrete answer to this, or even give some clues regarding how to proceed, as well as helpful references? Thanks in advance.