Fabian
Reputation
13,949
119/100 score
25 64
Impact
~308k people reached

 23 What is the 'implicit function theorem'? 22 What is the purpose of Stirling's approximation to a factorial? 20 Prove that $\sum_{k=1}^{\infty} \large\frac{k}{\text{e}^{2\pi k}-1}=\frac{1}{24}-\frac{1}{8\pi}$ 20 How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$? 19 Infinite powering by $i$

### Reputation (13,949)

 +10 How to see that if the following integral is finite, the second moment is finite as well? +10 Integrating $e^{a\cos(\phi_1-\phi_2)+b\cos(\phi_1-\phi_3)+c\cos(\phi_2-\phi_3)}$ over $[0,2\pi]^3$ +10 Relationship between short-time and large-frequency asymptotics in Fourier transform +10 Closed Form E[exp(x'Ax)]

### Questions (15)

 30 Simpler way to evaluate the Fourier transform of $\exp\left(i e^x\right)$? 22 Asymptotic expression of an oscillatory integral 7 What is u-substitution? 6 Connection between Legendre polynomial and Bessel function 6 Asymptotic expansion of integral involving modified Bessel-function

### Tags (180)

 255 integration × 78 90 definite-integrals × 24 245 calculus × 74 79 linear-algebra × 35 124 asymptotics × 27 73 sequences-and-series × 13 119 real-analysis × 21 70 probability × 16 111 complex-analysis × 42 65 limits × 17

### Accounts (8)

 Mathematics 13,949 rep 2564 Physics 1,188 rep 56 Mathematica 879 rep 614 MathOverflow 260 rep 27 Vi and Vim 128 rep 3