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In this paper, some new results are reported for the study of Riemann zetafunction $\zeta(s)$ 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 isto find that $\zeta(s)$ can be expressed as a linear combination of polynomialsof infinite degree, whose consequences are shown in several aspects: (i)numerically it provides a scenario to construct very fast convergent algorithmto calculate $\zeta(s)$; (ii) interestingly it shows that Lagrangeinterpolation using infinite number of integer Euler zeta functions reproducesthe exact complex $\zeta(s)$; (iii) surprisingly it demonstrates thatalternating Riemann zeta function (or other entire functions removing the poleof zeta function) is admissible to Melzak combinatorial transform forpolynomials. Applying the functional symmetry on $\zeta(s)$ in the form ofMelzak transform induces $\zeta(s)$ being written as the difference of twosymmetrized factorials whose zeros are proved to all have real part of 1/2.Furthermore, the two symmetrized factorials are proved to have interlacingbetween the two sequences of the imaginary part of their zeros on upper (orlower) half plane, which ensures the difference of the two symmetrizedfactorials [proportional to $\zeta(s)$] attaining the same feature of zeroswith real part of 1/2 to endorse Riemann hypothesis.

Riemann Zeta Function Expressed as the Difference of Two Symmetrized Factorials Whose Zeros All Have Real Part of 1/2