  We explore conformally coupled scalar theory in AdS$_{6}$ extensively and
their classical solutions by employing power expansion order by order in its
self-interaction coupling $\lambda$. We study holographic correlation functions
of scalar operator deformations to a certain 5-dimensional conformal field
theory where the operators share the same scaling dimension $\Delta=3$, from
the classical solutions. For our solutions, we choose a scheme where we remove
co-linear divergences of momenta along the AdS boundary directions which
frequently appear in the classical solutions. This shows clearly that the
holographic correlation functions are free from the co-linear divergences. It
turns out that this theory provides correct conformal 2- and 3- point functions
of the $\Delta=3$ scalar operators as expected in previous literature. It makes
sense since 2- and 3- point functions are determined by global conformal
symmetry not being dependent on the details of the conformal theory. We also
get 4-point function from this holographic model. In fact, it turns out that
the 4-point correlation function is not conformal because it does not satisfy
the special conformal Ward identity although it does dilation Ward identity and
respect $SO(5)$ rotation symmetry. However, in the co-linear limit that all the
external momenta are in a same direction, the 4-point function is conformal
which means that it satisfy the special conformal Ward identity. We inspect
holographic $n$-point functions of this theory which can be obtained by
employing a certain Feynman-like rule. This rule is a construction of $n$-point
function by connecting $l$-point functions each other where $l<n$. In the
co-linear limit, these $n$-point functions reproduce the conformal $n$-point
functions of $\Delta=3$ scalar operators in $d=5$ Euclidean space addressed in
arXiv:2001.05379.
