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Tolaso
  • Member for 7 years, 6 months
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28 votes
1 answer
1k views

Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$

18 votes
1 answer
368 views

Closed form of integral using contour integration

17 votes
1 answer
628 views

Integrate $\int_0^1 \frac{\ln(1+x^a)}{1+x}\, dx$

13 votes
2 answers
528 views

Closed form $\int_{-1}^{1} \frac{\ln (\sqrt{3} x +2)}{\sqrt{1-x^{2}} (\sqrt{3} x + 2)^{n}}\ dx$

12 votes
1 answer
452 views

integral $\int_0^{\pi} \left( \frac{\pi}{2} - x \right) \frac{\tan x}{x} \, {\rm d}x$

10 votes
2 answers
446 views

On the summation $\sum \limits_{n=1}^{\infty} \arctan \left ( \frac{1}{n^3+n^2+n+1} \right )$

10 votes
2 answers
355 views

Alternating series involving zeta function

9 votes
3 answers
794 views

A log arctan integral $\int_0^1 \log x \arctan^2 x \, dx$

8 votes
1 answer
156 views

An arctan series with roots $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} \arctan \frac{1}{n \sqrt{n}}$

8 votes
1 answer
174 views

Derivation of an integral result

8 votes
3 answers
171 views

A gamma summation: $\sum_{n=0}^{\infty} \frac{2}{\Gamma ( a + n) \Gamma ( a - n )} = \frac{2^{2a-2}}{\Gamma ( 2a - 1 )} + \frac{1}{\Gamma^2 (a)}$

8 votes
2 answers
490 views

Closed form of a series (dilogarithm)

7 votes
1 answer
253 views

The number $\sum\limits_{n=-\infty}^{\infty} \frac{1}{2^{n^2}}$ is transcendental

7 votes
1 answer
307 views

Closed form of series involving Fibonacci numbers

7 votes
6 answers
953 views

Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$ [duplicate]

7 votes
4 answers
567 views

Evaluation of integral $\int_{0}^{\infty}\frac{\sin x}{x\left ( 1+x^2 \right )^2}\,{\rm d}x$

7 votes
1 answer
3k views

Integration of $\ln $ around a keyhole contour

7 votes
1 answer
1k views

Double sum and zeta function

7 votes
0 answers
150 views

Integral with contours

7 votes
2 answers
241 views

On the series $\sum \limits_{n=-\infty}^{\infty} \frac{\cos n}{n^2+1}$.

7 votes
2 answers
321 views

On the Euler sum $\sum \limits_{n=1}^{\infty} \frac{H_n^{(4)} H_n^2}{n^6}$

7 votes
1 answer
465 views

Integral with trigonometric and dilogarithm

7 votes
5 answers
3k views

A limit without invoking L'Hopital: $\lim_{x \to 0} \frac{x \cos x - \sin x}{x^2}$

7 votes
1 answer
469 views

Evaluation of series $\sum \limits_{n=1}^{\infty} \frac{\arctan n}{n^2}$

6 votes
1 answer
640 views

$n$-th derivative of Beta function

6 votes
2 answers
568 views

Convergence of series of nested sequence

5 votes
1 answer
735 views

Proving $\pi \coth \pi a= \frac{1}{a}+ \sum_{n=1}^{\infty}\frac{2a}{n^2+a^2}$ using the Fourier series for $\cosh ax$

5 votes
3 answers
126 views

Evaluation of $5\times 5$ determinant

5 votes
2 answers
305 views

Closed form of $\ln^n \tan x\, dx$

5 votes
4 answers
680 views

Generalized Fresnel integral $\int_0^\infty \sin x^p \, {\rm d}x$

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