# Julián Aguirre

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I am a professor in the Math Department of the University of the Basque Country. I got my PhD at Washington University in St. Louis. My research interests are PDE's and Number Theory. My hobbies are sailing and travelling around the word.

 26 $\int_{0}^{\infty} \frac{e^{-x} \sin(x)}{x} dx$ Evaluate Integral 19 Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$ 16 Inverse of a bijection f is equal to its derivative 15 What is the difference between outer measure and Lebesgue measure? 14 graphs of functions which are closed, but fail to be continuous

# 20,348 Reputation

 +15 Stability of solution to first-order nonlinear differential equation +10 Showing $\int_0^{2\pi} \log|1-ae^{i\theta}|d\theta=0$ +35 How do I integrate this in terms of error function +10 Relation between Continuity and Uniform Continuity

# 3 Questions

 15 Is there a non-decreasing sequence $(a_n)$ such that $\sum 1/a_n=\infty$ and $\sum1/(n+a_n)<\infty$? 14 Does $\sum_{n=1}^\infty n^{-1-|\sin n|^a}$ converge for some $a\in(0,1)$? 14 If $p$ is prime, does there exist a positive integer $k$ such that $2^k\,p+1$ is also prime?

# 180 Tags

 281 real-analysis × 135 122 integration × 44 229 calculus × 82 117 analysis × 54 184 sequences-and-series × 70 97 functional-analysis × 49 145 differential-equations × 82 94 pde × 50 134 complex-analysis × 55 92 limits × 23

# 5 Accounts

 Mathematics 20,348 rep 11036 MathOverflow 1,215 rep 611 Mathematica 191 rep 3 Area 51 151 rep 1 TeX - LaTeX 101 rep