#riemannzetafunction — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #riemannzetafunction, aggregated by home.social.
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On Pi Day 2025, as you might recall, I introduced you (more or less) to 3Blue1Brown. Also known as Grant Sanderson.
If there's any better source of animated math presentations, than Mr. Sanderson, I'm unaware of it.
Key word: "animated." In addition, he is a warm, enthusiastic teacher. And of course he knows his stuff well—how else could he have made the truly fantastic animations?
I haven't watched them all yet. But so far, I especially like 2016's BUT WHAT IS THE RIEMANN ZETA FUNCTION? VISUALIZING ANALYTIC CONTINUATION and 2019's DIFFERENTIAL EQUATIONS, A TOURIST'S GUIDE | DE1.
I may never again be able to ponder some ideas they convey, without seeing those animations in my head. They're that perfect.
So give those two videos a try, if you're comfortable enough with the one I had shared on Pi Day...if now you want a couple which are more challenging. Maybe unforgettable, too.
#3Blue1Brown
#RiemannZetaFunction
#DifferentialEquations
#learninghttps://mindly.social/@setsly/114161481212443838
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Interesting integral! #Challenge
\[\displaystyle\int_0^1\dfrac{\ln (x)\ln(1-x)}{x(1-x)}\operatorname{Li}_2(x)\ dx=5\zeta(2)\zeta(3)-8\zeta(5)\]
Where \(\operatorname{Li}_2(x)\) denotes the dilogarithm (or Spence's function), and \(\zeta(x)\) denotes the Riemann zeta function.#ZetaFunction #Zeta #Dilogarithm #SpenceFunction #Polylogarithm #Integral #DefiniteIntegral #Integration #Integrals #RiemannZetaFunction #Logarithm #Function #LogarithmicFunction
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Interesting integral! #Challenge
\[\displaystyle\int_0^1\dfrac{\ln (x)\ln(1-x)}{x(1-x)}\operatorname{Li}_2(x)\ dx=5\zeta(2)\zeta(3)-8\zeta(5)\]
Where \(\operatorname{Li}_2(x)\) denotes the dilogarithm (or Spence's function), and \(\zeta(x)\) denotes the Riemann zeta function.#ZetaFunction #Zeta #Dilogarithm #SpenceFunction #Polylogarithm #Integral #DefiniteIntegral #Integration #Integrals #RiemannZetaFunction #Logarithm #Function #LogarithmicFunction
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PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory