关键词: Functional equation, Zeta function, Münts formula

Abstract:

In this article, the author derives a functional equation 

η(s)=[( /4)^s-1/22/  Γ(1-s)sin(  s/2)]η(1-s)    (1)

of the analytic function η(s) which is defined by 
η(s)=1^-s-3^-s-5^-s+7^-s+…                                (2)
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.

Key words: Functional equation, Zeta function, Münts formula