Is there any (simple) approximation of this Hypergeometric function: $ \_2F\_1((b-1)a,b;ba;x) $, where $0<x<1$ and $b>a>1$.


Thanks!



Approximation of $ _2F_1((b-1)a,b;ba;x) $
There are Pade approximations. See [these slides by Matala-aho.](http://cc.oulu.fi/~tma/TOKYOSLIDES.pdf) I believe the results in the classical case you are asking about are due to Grisha Chudnovsky (1979, cited in the slides).


