  To obtain the waveform template of gravitational waves (GWs), substantial
computational resources and exceedingly high precision are often required. In
the previous study [JCAP 11 (2023) 070], we efficiently and accurately
calculate GW fluxes of a particle in circular orbits around a Schwarzschild
black hole using the confluent Heun function. We extend the previous method to
calculate the asymptotic GW fluxes from a particle in generic orbits around a
near-extreme Kerr black hole. Especially when dealing with the computational
difficulties in large eccentricity $e=0.9$, higher spin $a=0.999$, higher
harmonic modes, and strong-field regions, our results are much better than the
results of the numerical integration method based on the Mano-Suzuki-Takasugi
method.
