DK20250213

有哪些有趣的数学公式?

Euler's Identity $$e^{i\pi} + 1 = 0$$ Ramanujan’s Series for π $$\frac{1}{\pi} = \sum_{n=0}^{\infty} \frac{(4n)! (1103 + 26390n)}{(n!)^4 396^{4n}}$$ Gauss-Bernoulli Series $$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$$ Ramanujan’s Magical Identity $$\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^2} = \frac{\pi^2}{8}$$