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单词 FunctionalEquationOfTheRiemannZetaFunction
释义

functional equation of the Riemann zeta function


Let Γ denote the gamma functionDlmfDlmfMathworldPlanetmath, ζ the Riemann zeta functionDlmfDlmfMathworldPlanetmath and s any complex numberPlanetmathPlanetmath. Then

πs-12Γ(1-s2)ζ(1-s)=π-s2Γ(s2)ζ(s).

Though the equation appears too intricate to be of any use, the inherent in the formula makes this the simplest method of evaluating ζ(s) at points to the left of the critical stripMathworldPlanetmath.

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更新时间:2025/5/4 15:07:34