Chord complexity: Difference between revisions
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<math>\displaystyle D_s(a, b) = \frac{(ab)^{s/2}}{(a/b)^{s/2} + (b/a)^{s/2}}</math> | <math>\displaystyle D_s(a, b) = \frac{(ab)^{s/2}}{(a/b)^{s/2} + (b/a)^{s/2}}</math> | ||
By using the hyperbolic trigonometric identity <math>\cosh x = (e^x + e^{-x})/2</math>, that denominator can be rewritten in terms of the <math>\cosh</math> function as follows: | |||
<math>\displaystyle (a/b)^{s/2} + (b/a)^{s/2} = 2 \cosh(s/2 \log(b/a))</math> | <math>\displaystyle (a/b)^{s/2} + (b/a)^{s/2} = 2 \cosh(s/2 \log(b/a))</math> | ||