# Gauss hypergeometric function derivative

1. Jun 18, 2012

### fred_91

1. The problem statement, all variables and given/known data

I want to differentiate the Gauss hypergeometric function:
$_2F_1[a,b;c;\frac{k-x}{z-x}]$
with respect to z
2. Relevant equations

The derivative of
$_2F_1[a,b;c;z]$
with respect to z is:
$\frac{ab}{c} _2F_1[1+a,1+b;1+c;z]$

3. The attempt at a solution
Can I treat this as any other function, i.e., the same as with z in the fourth parameter but multiplied by the derivative of the fourth parameter:

$\frac{ab}{c} _2F_1[a,b;c;\frac{k-x}{z-x}]\frac{-(k-x)}{(z-x)^2}$

If the fourth parameter was sin(z). Would the derivative of
$_2F_1[a,b;c;\sin(z)]$
with respect to z
be
$\frac{ab}{c} _2F_1[1+a,1+b;1+c;sin(z)]cos(z)$?