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In this article we present the post-Newtonian (pN) coefficients of the energyflux (and angular momentum flux) at infinity and event horizon for a particlein circular, equatorial orbits about a Kerr black hole (of mass $M$ andspin-parameter $a$) up to 20-pN order. When a pN term is not a polynomial in$a/M$ and includes irrational functions (like polygamma functions), it iswritten as a power series of $a/M$. This is achieved by calculating the fluxesnumerically with an accuracy greater than 1 part in $10^{600}$. Such highaccuracy allows us to extract analytical values of pN coefficients that arelinear combinations of transcendentals like the Euler constant, logarithms ofprime numbers and powers of $\pi$. We also present the 22-pN expansion(spin-independent pN expansion) of the ingoing energy flux at the event horizonfor a particle in circular orbit about a Schwarzschild black hole.

Gravitational-wave flux for a particle orbiting a Kerr black hole to 20th post-Newtonian order: a numerical approach