  In this paper, some new results are reported for the study of Riemann zeta
function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$
expressed in a generalized Euler product only involving prime numbers.
Particularly, some new absolutely convergent series representations of
$\zeta(s)$ based on binomial expansion are presented. The crucial progress is
to find that $\zeta(s)$ can be expressed as a linear combination of polynomials
of infinite degree, whose consequences are shown in several aspects: (i)
numerically it provides a scenario to construct very fast convergent algorithm
to calculate $\zeta(s)$; (ii) interestingly it shows that Lagrange
interpolation using infinite number of integer Euler zeta functions reproduces
the exact complex $\zeta(s)$; (iii) surprisingly it demonstrates that
alternating Riemann zeta function (or other entire functions removing the pole
of zeta function) is admissible to Melzak combinatorial transform for
polynomials. Applying the functional symmetry on $\zeta(s)$ in the form of
Melzak transform induces $\zeta(s)$ being written as the difference of two
symmetrized factorials whose zeros are proved to all have real part of 1/2.
Furthermore, the two symmetrized factorials are proved to have interlacing
between the two sequences of the imaginary part of their zeros on upper (or
lower) half plane, which ensures the difference of the two symmetrized
factorials [proportional to $\zeta(s)$] attaining the same feature of zeros
with real part of 1/2 to endorse Riemann hypothesis.
