  We have developed a fully coupled-channel complex scaling method (ccCSM) for
the study of the most essential kaonic nucleus, $``K^-pp,"$ which is a resonant
state of a $\bar{K}NN$-$\pi\Sigma N$-$\pi\Lambda N$ coupled-channel system
based on a theoretical viewpoint. By employing the ccCSM and imposing the
correct boundary condition of resonance, the coupled-channel problem is
completely solved using a phenomenological energy-independent potential. As a
result of the ccCSM calculation of $``K^-pp,"$ in which all three channels are
treated explicitly, we have obtained three-body resonance as a Gamow state. The
resonance pole indicates that the binding energy of $``K^-pp"$ and the half
value of its mesonic decay width are 51 MeV and 16 MeV, respectively. In the
analysis of the resonant wave function obtained using the ccCSM, we clarify the
spatial configuration and channel compositions of $``K^-pp."$ Compared with
past studies of single-channel calculations based on effective $\bar{K}N$
potentials, the current study provides a guideline for the determination of the
$\bar{K}N$ energy to be used in effective potentials.
