Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
48 followers · 164 posts · Server mathstodon.xyzHow to prove this?!🤔
\[\displaystyle\int_\tfrac{1}{2}^1\dfrac{\psi(x)}{1+\Gamma^2(x)}dx=\ln\left(\sqrt{\dfrac{1+\pi}{2\pi}}\right)\]
where \(\Gamma(x)\) and \(\psi(x)\) are the gamma and digamma functions respectively.
#Integral #definiteintegral #gammafunction #digammafunction #pi #logarithm
#logarithm #pi #digammafunction #gammafunction #definiteintegral #integral
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
36 followers · 117 posts · Server mathstodon.xyzThe Riemann hypothesis, explained by Jørgen Veisdal: 🔗 https://www.cantorsparadise.com/the-riemann-hypothesis-explained-fa01c1f75d3f
\[\zeta(s)=0;\ s\notin2\mathbb{Z}^-\implies\Re(s)=\dfrac{1}{2}\]
#RiemannHypothesis #Riemann #Hypothesis #Atiyah #NumberTheory #Conjecture #AnalyticNumberTheory #Mathematics #CantorsParadise #OpenProblem #UnsolvedProblem #PrimeNumber #RiemannZetaFunction #ZetaFunction #NonTrivialZero #LogarithmicIntegral #XiFunction #PrimeNumberTheorem #PrimeNumberDistribution #PrimeCountingFunction #GammaFunction
#gammafunction #primecountingfunction #primenumberdistribution #primenumbertheorem #xifunction #logarithmicintegral #nontrivialzero #zetafunction #riemannzetafunction #primenumber #unsolvedproblem #openproblem #cantorsparadise #mathematics #analyticnumbertheory #conjecture #numbertheory #atiyah #hypothesis #riemann #riemannhypothesis