I'm looking for a book, set of tables, or other reference which contains a comprehensive list of hypergeometric identities; that is, something which allows a hypergeometric fucntion to be expressed in terms of elementary or other known special functions.
For example, from Wikipedia:
$\log(1+z)=z\,_2F_1(1,1;2;-z)$
$(1-z)^{-a} = \,_2F_1(a,b;b;z)$
$\arcsin z = z \,_2F_1\left(\tfrac{1}{2}, \tfrac{1}{2}; \tfrac{3}{2};z^2\right)$
Now I should mention that Wolfram Alpha and presumably mathematica can also do this; Here's an example. However, I would like a written reference, preferably in table form, and either with its own proofs of identities, or with references to sources containing proofs.
Does anyone know of any such "dictionaries" for Hypergeometric functions?
Best Answer
Have a look here; in particular, see this subsection (Special Cases). Note that you can find more information by pressing the $i$ symbols on the right.