156 Funny identities 101 Why is Euler's Gamma function the “best” extension of the factorial function to the reals? 70 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ 51 Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$ 51 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)

Reputation (6,333)

 +10 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? +30 Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$ +10 Volumes of n-balls: what is so special about n=5? +10 Domain of the Gamma function

Question (1)

 71 Volumes of n-balls: what is so special about n=5?

Tags (44)

 237 real-analysis × 6 124 special-functions × 5 181 calculus × 6 108 gamma-function × 2 156 integration × 5 101 education 156 improper-integrals × 4 70 gaussian-integral 138 analysis × 7 54 definite-integrals × 2