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 ?

This post imported from StackExchange Mathematics at 2016-08-23 15:26 (UTC), posted by SE-user Jaswin