it is posible to calculate $$\int_0^{\infty } \frac{x^{z-1}}{q^x-1} \, dx$$ as Mellin transform Mathematica could not do it
2026-03-25 21:44:58.1774475098
Mellin transform q series
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Substitute $t=x\log q$ to get $$\int_0^{\infty} \frac{1}{\ln^{z}q}\frac{t^{z-1}}{e^t-1}dt=\Gamma(z)\zeta(z)\frac{1}{\ln^{z}q}$$