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Paramanand Singh
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  • Member for 9 years, 2 months
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81 votes
3 answers
5k views

Denesting radicals like $\sqrt[3]{\sqrt[3]{2} - 1}$

53 votes
14 answers
5k views

Simplest way to get the lower bound $\pi > 3.14$

45 votes
2 answers
3k views

An infinite series plus a continued fraction by Ramanujan

42 votes
2 answers
7k views

What is the use of hyperreal numbers?

32 votes
7 answers
17k views

A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$

25 votes
4 answers
3k views

Proof of a Ramanujan Integral

25 votes
4 answers
3k views

Sum the series $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$

25 votes
1 answer
2k views

Gosper's unusual formula connecting $e$ and $\pi$

25 votes
2 answers
9k views

Taylor's Theorem with Peano's Form of Remainder

23 votes
1 answer
525 views

A problem posed by Ramanujan involving $\sum e^{-5\pi n^2}$

22 votes
1 answer
783 views

Sum the series $\sum_{n = 0}^{\infty} (-1)^{n}\{(2n + 1)^{7}\cosh((2n + 1)\pi\sqrt{3}/2)\}^{-1}$

19 votes
1 answer
2k views

An alternative proof of Cauchy's Mean Value Theorem

19 votes
1 answer
607 views

Another Ramanujan's formula dealing with $\coth^{2}(5\pi)$

19 votes
6 answers
3k views

For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.

19 votes
3 answers
3k views

Monotone functions and non-vanishing of derivative

16 votes
2 answers
431 views

If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$

15 votes
2 answers
2k views

Doubt regarding proof that $\mathbb{Z}, \mathbb{Z}[x]$ are unique factorization domains

15 votes
2 answers
465 views

Ramanujan's series $1+\sum_{n=1}^{\infty}(8n+1)\left(\frac{1\cdot 5\cdots (4n-3)}{4\cdot 8\cdots (4n)}\right)^{4}$

14 votes
3 answers
2k views

Continuous decreasing function has a fixed point

14 votes
1 answer
570 views

Continued fraction estimation of error in Leibniz series for $\pi$.

14 votes
2 answers
698 views

Bellard's exotic formula for $\pi$

14 votes
1 answer
791 views

Unsolvability of a Quintic and its link with "Simplicity" of $A_{5}$

14 votes
3 answers
1k views

Show that $\sum\limits_n1/x_{n}^{2} = 1/10$ where $x_{n}$ is the $n^{\text{th}}$ positive root of $\tan x = x$ [duplicate]

13 votes
4 answers
4k views

Continued fraction for $\tan(nx)$

13 votes
0 answers
229 views

Bi-linear relation between two continued fractions

13 votes
2 answers
446 views

Limit of $\sin (a^{n}\theta\pi)$ as $ n \to \infty$ where $a$ is an integer greater than $2$

12 votes
1 answer
615 views

Integral formula for $\int_{0}^{\infty}e^{-3\pi x^{2}}((\sinh \pi x)/(\sinh 3\pi x))\,dx$ by Ramanujan

11 votes
1 answer
441 views

Ramanujan's transformation formula connected with $r_{2}(n)$

11 votes
1 answer
238 views

If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$

11 votes
1 answer
572 views

Evaluation of complete elliptic integrals $K(k) $ for $k=\tan(\pi/8),\sin(\pi/12)$