#infiniteproduct

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• An interesting infinite product! \[\displaystyle\prod_{n=1}^\infty\coth^{(-1)^n}\left(\dfrac{\pi n}{2}\right)=\dfrac{\sqrt\pi}{\sqrt[4]2\sqrt{\varpi}}\] where \(\varpi=2.62205755\ldots\) is the lemniscate constant (the ratio of the perimete

  Pustam | पुस्तम | পুস্তম🇳🇵@[email protected]♥ 1↻ 12024-05-12 10:58 UTCView post →

• For any integer \(n\geq3\), \[\left\lfloor\dfrac{1}{1-\displaystyle\prod_{k=n}^\infty\left(1-\dfrac{1}{F_k}\right)}\right\rfloor=F_{n-2}\] where \(F_n\) is the \(n\)-th Fibonacci number. #FibonacciNumber #Fibonacci #FibonacciSequence #Fibon

  Pustam | पुस्तम | পুস্তম🇳🇵@[email protected]♥ 0↻ 02024-05-09 09:08 UTCView post →

• 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\mathb

  Pustam | पुस्तम | পুস্তম🇳🇵@[email protected]♥ 0↻ 12023-01-04 06:19 UTCView post →