Acta mathematica scientia, Series B >
ON A FUNCTIONAL EQUATION
Received date: 2007-02-05
Online published: 2009-03-20
Supported by
Supported by Separated Budget Research from New Jersey City University.
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
Ding Yi . ON A FUNCTIONAL EQUATION[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 225 -231 . DOI: 10.1016/S0252-9602(09)60023-0
[1] Titchmarsh E C. Introduction to the Theory of Fourier Integrals. Oxford, 1948
[2] Titchmarsh E C. The Theory of the Riemann Zeta-Function. Oxford, 1951
[3] Ding Yi. Distribution form of Ramanujan Identity (preprint)
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