In my notes I have written down the following relation:
$_2F_1(a,a+\frac{1}{2};c;z)=2^{c-1}z^{(1-c)/2}(1-z)^{-a+(c-1)/2}L_{2a-c}^{1-c}\big(\frac{1}{\sqrt{1-z}}\big)\ ,$
where $_2F_1(a,b;c;z)$ is the hypergeometric function and $L_{\alpha}^{\beta}(z)$ is the associated Legendre polynomial. I then use this for the special case $c=1$, reducing to the normal Legendre polynomial.
However now I can't confirm the above identity. I've looked through Wikipedia, Mathworld, Wolfram functions and dlfm, to no avail.
Am I missing it in those sites, or did I get it somewhere else? Did I make it up? Does it refer to another function than Legendre?