I am self teaching myself python and computational physics via Mark Newmans book Computational Physics the exercise is 5.17 of Computational Physics. I have to shift the limits of integration for an improper integral after a change of variables so that Gaussian quadrature method gives a more accurate result. I am suppose to approximate the Gamma function $\Gamma(a)$
The relevant equation is here:
This is the question:
When I isolate for $x$ I get $x = \frac{zc}{1-x}$. But when $z = \frac{1}{2}$ I get $x = c$ but this makes no sense because this implies z is a constant which it's not. I know in order to shift a function $f(x)$ to the left you $f(x + c)$ but how would I do this with an integrand?