High Quality Content by WIKIPEDIA articles! In mathematics, the L-functions of number theory are expected to have several characteristic properties, one of which is that they satisfy certain functional equations. There is an elaborate theory of what these equations should be, much of which is still conjectural. For example, the Riemann zeta function has a functional equation relating its value at the complex number s with its value at 1 ? s. In every case this relates to some value ?(s) that is only defined by analytic continuation from the infinite series definition.

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