Difference between revisions of "Relationship between integral of x*log(sin(x)), and Apéry's constant, pi, and logarithm"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\int_0^{\frac{\pi}{2}} x \log(\sin(x)) dx = \dfrac{7}{16}\zeta(3) - \dfrac{\pi^2}{8} \log(2).$$ ==Proof== ==Reference...") |
(No difference)
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Revision as of 17:17, 24 June 2016
Theorem
The following formula holds: $$\displaystyle\int_0^{\frac{\pi}{2}} x \log(\sin(x)) dx = \dfrac{7}{16}\zeta(3) - \dfrac{\pi^2}{8} \log(2).$$
