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

+ 3 like - 0 dislike
2795 views

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
@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
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsO$\varnothing$erflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.