# What property of Hypergeometric function is used in this paper?

I was going through the following paper, Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime - Balasubramanian, Kraus, Lawrence, 9805171v4. http://arxiv.org/pdf/hep-th/9805171.pdf

While finding scalar field solutions in global coordinates which is of the form, $z^{2h}(1-z)^{2b} 2F1[A,B,C,z]$ they find two roots for $h$ and $b$ each(page 9, below eqn (26)).

$A$, $B$, $C$ are functions of $h$ and $b$ and dimension in which we are working. And they claim that only two independent solutions exist for Hypergeometric functions. But shouldn't there be (4) four solutions, for each combinations of $h$ and $b$? They say that the solutions depend on only the indicial roots of $b$, and hence later on the same page they chose one root of $h$ without loss of generality which I don't understand. Can someone help me with the choice ?

• The down vote may be because the question is more appropriate in mathematics?
– jim
Aug 20, 2016 at 20:24
• @jim or possibly because it's not clear, and one has to go find that paper to see what's happening. For example what is $a$? Did you mean that $A,B,C$ are functions of $h$ and $b$? Otherwise what has $h$ got to do with the roots? Apart from the cases $h>0$ and $h\leq 0$ of course. I didn't downvote but I don't find this post clear as is Aug 20, 2016 at 20:48
• Is it fine now ? Aug 21, 2016 at 4:39