Andrey Rekalo
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 134 Funny identities 79 Why is Euler's Gamma function the “best” extension of the factorial function to the reals? 51 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \dfrac{\sqrt \pi}{2}$ 37 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ 36 Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$

### Reputation (5,112)

 +10 Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$ +15 Volumes of n-balls: what is so special about n=5? +10 An orthonormal set cannot be a basis in an infinite dimension vector space? +10 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis

### Question (1)

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

### Tags (42)

 184 real-analysis × 6 89 improper-integrals × 3 130 calculus × 6 85 gamma-function × 2 116 integration × 5 79 education 99 analysis × 7 38 definite-integrals × 2 99 special-functions × 4 37 sequences-and-series × 3

### Accounts (8)

 MathOverflow 17,186 rep 861107 Mathematics 5,112 rep 22839 Quantitative Finance♦ 2,965 rep 62947 Area 51 201 rep 13 Stack Overflow 176 rep 14