James Arathoon's user avatar
James Arathoon's user avatar
James Arathoon's user avatar
James Arathoon
  • Member for 5 years, 4 months
  • Last seen this week
  • Ceredigion, United Kingdom
21 votes
Accepted

Number which is simultaneously sum of 2 and 3 squares

11 votes

Evaluate $\int_{0}^{\pi} \frac{x\coth x-1}{x^2}dx$

6 votes

An intriguing pattern in Ramanujan's theory of elliptic functions that stops?

6 votes
Accepted

Find all integers n such that $(\frac{n^3-1}{5})$ is prime

5 votes

A closed form for: $\int_{0}^{\infty} \frac{1}{(x-\log x)^2}dx$

4 votes

The sum of the series $ \cos(x)-\cos(2x)+\cos(3x)-...$

4 votes

Challenging integral $\int_{0}^{1}\frac{x\operatorname{li}(x)}{x^2+1}dx$

4 votes

Special properties of the number $146$

4 votes

Show that for any natural number n between $n^2$ and$(n+1)^2$ there exist 3 distinct natural numbers a, b, c, so that $a^2+b^2$ is divisible by c

3 votes
Accepted

How to evaluate closed form for this sum $\sum_{k=1}^{\infty}{k\over [(pk)^2-1][(qk)^2-1]}?$

3 votes
Accepted

Representing a given number as the sum of two squares.

3 votes

Evaluate the integral $\int x \tan(x)\mathrm{d}x$

3 votes

How to turn number into sum of unique primes?

3 votes
Accepted

Series expansion of $\tan^2$ and $\tanh^2$

3 votes

Egyptian fractions: does the greedy algorithm never give more fractions than absolutely necessary?

3 votes

Evaluating the series $\sum_{n=1}^{‎\infty‎}\frac{\pi^n}{n!n^p}B_n(z)$, when $z=0$ or $z=1$.

3 votes
Accepted

Proof of a Zeta function identity

3 votes
Accepted

Is this a new formula for Pell numbers?

3 votes

Yet another difficult logarithmic integral

3 votes

Find a closed form of $\sum_{n=1}^{\infty} \frac{{H_{n-1}^{(2)}}x^{2n}}{n^2{{2n}\choose{n}}}$.

3 votes

Pythagorean triples conditions

3 votes

Closed form of the sum $\sum_{n=1}^{\infty}\frac{H_n}{n^x}$

3 votes

Is there an exact solution for $\large\int \frac{dx}{\tan^{-1}(x)}$?

3 votes
Accepted

On a better solution for $\large {\int_{-x}^x\frac{dx}{\sqrt {1-x^2} e^{bx^2+ax}}}$

2 votes

Please provide a function approximating the following hypergeometric series?

2 votes
Accepted

Is there a name for the following type of infinite series function?

2 votes

show $\int \frac{1}{\cosh(x)}dx = \arctan(\sinh(x))$ using the substitution $u=\sinh(x)$

2 votes

Are there incongruent pythagorean triangles with the same perimeter and same area?

2 votes

How to show that $\int_{0}^{\infty}\ln^2\left(\frac{e^x+1}{e^x-1}\right)dx=\frac{7\zeta(3)}{2}$?

2 votes

Could this integral expression for $\zeta(3)$ be simplified any further?

1
2 3 4 5