The Riemann zeta function and tuning: Difference between revisions
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ArrowHead294 (talk | contribs) m →Relationship to harmonic entropy: Missing parentheses |
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The expression | The expression | ||
<math>\displaystyle{\left|\zeta\frac{1}{2} + it)\right|^2 \cdot \overline {\phi(t)}}</math> | <math>\displaystyle{\left|\zeta\left(\frac{1}{2} + it\right)\right|^2 \cdot \overline {\phi(t)}}</math> | ||
is, up to a flip in sign, the Fourier transform of the unnormalized Harmonic Shannon Entropy for {{nowrap|''N'' {{=}} ∞}}</math>, where φ(''t'') is the characteristic function (aka Fourier transform) of the spreading distribution and {{overline|φ(''t'')}} denotes complex conjugation. | is, up to a flip in sign, the Fourier transform of the unnormalized Harmonic Shannon Entropy for {{nowrap|''N'' {{=}} ∞}}</math>, where φ(''t'') is the characteristic function (aka Fourier transform) of the spreading distribution and {{overline|φ(''t'')}} denotes complex conjugation. | ||