On a functional equation

In this article, the author derives a functional equation equation(1)η(s) = [(π4)s-122πΓ(1-s) sin(πs2)] η (1-s)of the analytic function η(s) which is defined by equation(2)η(s) = 1-s-3-s -5-s+7-s+ …η(s) = 1-s-3-s -5-s+7-s+ …for complex variable s with Re s > 1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.