Antonio Vargas
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 31 Evaluate:: $2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right)$ 26 Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$ 26 Derivation of asymptotic solution of $\tan(x) = x$. 21 Rounding is asymptotically useless? 18 Finding $\displaystyle \lim_{n \to \infty} \int_0^\infty \frac{e^{-x}\cos{x}}{nx^2 + \frac{1}{n}}dx$

### Reputation (17,987)

 -2 Choice of $q$ in Baby Rudin's Example 1.1 +10 Approximation to the Lambert W function +10 Specific path in a gradient field of a saddle +10 How to estimate the growth of a “savage” function near 1?

### Questions (36)

 19 Asymptotic analysis of the integral $\int_0^1 \exp\{n (t+\log t) + \sqrt{n} wt\}\,dt$ 14 If $\lambda_n \sim \mu_n$, is it true that $\sum \exp(-\lambda_n x) \sim \sum \exp(-\mu_n x)$ as $x \to 0$? 13 Showing that $\gamma = -\int_0^{\infty} e^{-t} \log t \,dt$, where $\gamma$ is the Euler-Mascheroni constant. 12 Eigenvalues and eigenfunctions for the Fredholm integral operator $K(g) = \int_0^1 e^{x t} g(t) dt$. 12 Estimating the integral $\int_0^1 (1-t^2)^{-1/2} e^{-nt} \,dt$ for large $n$.

### Tags (166)

 372 asymptotics × 148 149 calculus × 56 278 roots × 73 135 integration × 44 254 complex-analysis × 91 128 limits × 50 227 sequences-and-series × 57 116 polynomials × 34 177 real-analysis × 56 92 approximation × 30

### Accounts (24)

 Mathematics 17,987 rep 23686 Mathematica 278 rep 27 MathOverflow 199 rep 9 Academia 182 rep 16 Stack Apps 178 rep 7