I need to evaluate the complex line integrals in the following equation: $$g(z)=\frac{\int_0^z\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}{\int_0^1\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}.$$ Can someone advise me on how to evaluate this expression on Wolfram? For those interested in the background, the source of the above equation is "Conformal mapping between two right-angled triangles". If not possible on Wolfram, is there an alternate means to evaluate this?
2026-03-26 03:18:42.1774495122
How can I evaluate this complex integral equation on Wolfram?
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In this case, Mathematica seems to have no trouble performing the integral directly: