Antonio Vargas

Halifax, Canada

http://mathstat.dal.ca/~antoniov/

I like studying the zeros of functions. Here's a list of my answers on the topic here on Math.SE. I also enjoy answering questions about asymptotics in general.

Check out my attempt to add real-time previews for comments here on Stack Exchange.

My avatar is cropped from this image by Garyck Arntzen.

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How can I make points "glow"?

plotting graphics asked Mar 7, 2013 at 22:39

mathematica.stackexchange.com

25 votes

Showing that $\gamma = -\int_0^{\infty} e^{-t} \log t \,dt$, where $\gamma$ is the Euler-Mascheroni constant.

calculus real-analysis analysis asked Feb 23, 2012 at 4:54

math.stackexchange.com

22 votes

Eigenvalues and eigenfunctions for the Fredholm integral operator $K(g) = \int_0^1 e^{x t} g(t) \, dt$.

analysis functional-analysis integral-equations asked Feb 11, 2012 at 21:30

math.stackexchange.com

22 votes

Asymptotic analysis of the integral $\int_0^1 \exp\{n (t+\log t) + \sqrt{n} wt\}\,dt$

complex-analysis integration asymptotics asked Sep 16, 2012 at 15:52

math.stackexchange.com

21 votes

Showing a function is measurable in a product measure space

measure-theory asked Dec 2, 2012 at 23:18

math.stackexchange.com

14 votes

If $\lambda_n \sim \mu_n$, is it true that $\sum \exp(-\lambda_n x) \sim \sum \exp(-\mu_n x)$ as $x \to 0$?

real-analysis sequences-and-series analysis asymptotics asked Jan 13, 2013 at 18:04

math.stackexchange.com

12 votes

Estimating the integral $\int_0^1 (1-t^2)^{-1/2} e^{-nt} \,dt$ for large $n$.

asymptotics asked Jan 18, 2012 at 2:58

math.stackexchange.com

11 votes

Determining the action of the operator $D\left(z, \frac d{dz}\right)$

analysis lie-algebras operator-theory differential-operators asked Apr 1, 2012 at 19:15

math.stackexchange.com

10 votes

Showing a sequence of integrals converges to zero

complex-analysis functional-analysis proof-verification singular-integrals asked Feb 7, 2015 at 23:25

math.stackexchange.com

9 votes

About B. Ya Levin's proof that $|f(x)| \leq M$ implies $|f(x+iy)| \leq Me^{\sigma y}$

complex-analysis inequality asked Mar 24, 2014 at 21:14

math.stackexchange.com

Top Answers

Derivation of asymptotic solution of $\tan(x) = x$.

math.stackexchange.com

Approximation to the Lambert W function

math.stackexchange.com

Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $

math.stackexchange.com

Choice of $q$ in Baby Rudin's Example 1.1

math.stackexchange.com

Calculating a real integral using complex integration

math.stackexchange.com

Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$

math.stackexchange.com

What's the behaviour of $I_n=\int_0^1\left(\frac1{\log x}+\frac1{1-x}\right)^ndx$, as $n \to \infty$?

math.stackexchange.com

Patterns of the zeros of the Faulhaber polynomials (modified)

math.stackexchange.com

$\lambda-z-e^{-z}=0$ has one solution in the right half plane

math.stackexchange.com

Number of real positive roots of a polynomial?

math.stackexchange.com

Rounding is asymptotically useless?

math.stackexchange.com

Partial sum of the harmonic series between two consecutive fibonacci numbers

math.stackexchange.com

Finding the Number of Zeros of a Function in a Given Annulus

math.stackexchange.com

Complex zeros of the polynomials $\sum_{k=0}^{n} z^k/k!$, inside balls

math.stackexchange.com

How to understand intuitively the Stolz-Cesaro Theorem for sequences?

math.stackexchange.com

Roots of $\frac{z^n-1}{z-1}=b$

math.stackexchange.com

Finding $\displaystyle \lim_{n \to \infty} \int_0^\infty \frac{e^{-x}\cos{x}}{nx^2 + \frac{1}{n}}dx$

math.stackexchange.com

Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$

math.stackexchange.com

Approximating roots of the truncated Taylor series of $\exp$ by values of the Lambert W function

math.stackexchange.com

Is there a closed form for the series $\sum_{k=1}^\infty \frac{\ln(4k-3)}{(4k-3)}-\frac{\ln(4k-1)}{(4k-1)}?$

math.stackexchange.com

Fitting a closed curve on the roots of ${x \choose k}-c$

math.stackexchange.com

Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$

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Integral for function of square

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What does this $\asymp$ symbol mean? (subject: analytic number theory)

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Asymptotic evaluation of integral method of steepest descent

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What is the most efficient method to evaluate this indefinite integral?

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Method of dominant balance and perturbation

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Find the integral part of $\sum_{i=2}^{10000}\frac1{\sqrt{i}}$

math.stackexchange.com

let PageDown and MathJax work together

stackoverflow.com

Closed Form for $~\lim\limits_{n\to\infty}~\sqrt n\cdot(-e)^{-n}\cdot\sum\limits_{k=0}^n\frac{(-n)^k}{k!}$

math.stackexchange.com