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Mark Viola
  • Member for 7 years, 4 months
  • Last seen this week
  • The Woodlands, TX
27 votes
6 answers
2k views

Real-Analysis Methods to Evaluate $\int_0^\infty \frac{x^a}{1+x^2}\,dx$, $|a|<1$.

12 votes
0 answers
406 views

An Extended Frullani Integral

10 votes
0 answers
724 views

Methodologies to Evaluate $\lim_{L\to \infty}\int_0^\infty \frac{\sin(Lx)}{x}\cos(x^3/3)\,dx$

9 votes
4 answers
740 views

Real Analysis Methodologies to show $\gamma =2\int_0^\infty \frac{\cos(x^2)-\cos(x)}{x}\,dx$

9 votes
0 answers
1k views

Asymptotic large order approximation for Bessel function expression

8 votes
3 answers
323 views

Evaluation of $\sum_{n=1}^\infty \frac{(-1)^{n-1}\eta(n)}{n} $ without using the Wallis Product

5 votes
3 answers
370 views

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

4 votes
4 answers
325 views

Alternative approaches to showing that $\gamma=\int_0^\infty \left(\frac{1}{1+x^a}-\frac{1}{e^x}\right)\,\frac1x\,dx$, $a>0$

3 votes
1 answer
277 views

Real Analysis Methodologies to Prove $-\int_x^\infty \frac{\cos(t)}{t}\,dt=\gamma+\log(x)+\int_0^x \frac{\cos(t)-1}{t}\,dt$ for $x>0$