User Paramanand Singh

38

59

votes

2

answers

3k

views

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

Oct 5 '17 at 8:35 Michael Rozenberg 113k

21

46

votes

14

answers

3k

views

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

real-analysis sequences-and-series inequality pi upper-lower-bounds

Aug 27 at 14:47 Jack D'Aurizio 294k

24

39

votes

2

answers

2k

views

An infinite series plus a continued fraction by Ramanujan

sequences-and-series continued-fractions

Jun 17 '17 at 3:05 Paramanand Singh 52.1k

27

29

votes

7

answers

7k

views

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

calculus limits alternative-proof

Aug 9 '17 at 16:34 aetzbar 1

6

24

votes

2

answers

3k

views

What is the use of hyperreal numbers?

analysis epsilon-delta nonstandard-analysis infinitesimals

Jan 24 '18 at 15:08 Mikhail Katz 30.9k

9

24

votes

1

answer

1k

views

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

sequences-and-series pi

Oct 2 '16 at 11:27 Tito Piezas III 28.3k

20

22

votes

4

answers

2k

views

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

sequences-and-series

Feb 21 '17 at 11:25 Community♦ 1

18

19

votes

2

answers

4k

views

Taylor's Theorem with Peano's Form of Remainder

calculus

Jun 11 '18 at 8:38 Oskar Limka 855

12

19

votes

1

answer

559

views

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

sequences-and-series

Nov 11 '15 at 14:42 Nemo 3,205

16

18

votes

2

answers

2k

views

Proof of a Ramanujan Integral

calculus definite-integrals improper-integrals

Feb 18 '15 at 18:09 Community♦ 1

7

16

votes

1

answer

524

views

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

sequences-and-series

Apr 25 '15 at 10:43 Community♦ 1

6

14

votes

1

answer

842

views

An alternative proof of Cauchy's Mean Value Theorem

calculus real-analysis

Mar 25 '18 at 22:23 Maths Survivor 502

6

14

votes

1

answer

370

views

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

calculus reference-request pi continued-fractions

Jul 20 '15 at 3:38 Community♦ 1

4

14

votes

2

answers

563

views

Bellard's exotic formula for $\pi$

soft-question pi

Jun 21 '15 at 5:01 Community♦ 1

7

14

votes

4

answers

1k

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.

calculus real-analysis

Feb 16 '14 at 8:31 Paramanand Singh 52.1k

11

13

votes

3

answers

1k

views

Monotone functions and non-vanishing of derivative

calculus real-analysis

Jul 1 '16 at 16:28 David C. Ullrich 62.4k

7

13

votes

1

answer

488

views

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

abstract-algebra galois-theory

Jul 6 '15 at 11:05 Paramanand Singh 52.1k

7

13

votes

2

answers

322

views

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

calculus real-analysis ordinary-differential-equations limits convergence

Sep 22 '14 at 21:06 Yiorgos S. Smyrlis 64k

5

13

votes

3

answers

527

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]

sequences-and-series

Jun 29 '14 at 10:39 Community♦ 1

2

12

votes

0

answers

207

views

Bi-linear relation between two continued fractions

continued-fractions

Aug 19 '15 at 21:26 Community♦ 1

3

12

votes

3

answers

992

views

Continuous decreasing function has a fixed point

calculus real-analysis

Mar 23 '14 at 11:34 Dejan Govc 13k

12

votes

1

answer

334

views

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

calculus

Jul 20 '13 at 15:32 Martin Argerami 132k

8

11

votes

2

answers

275

views

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

sequences-and-series

Feb 9 '18 at 16:48 Paramanand Singh 52.1k

5

11

votes

2

answers

129

views

Function satisfying $\lim_{x\to 0}\frac{f(ax)}{f(x)}=a$

calculus real-analysis

Jan 18 '17 at 18:05 Community♦ 1

9

11

votes

1

answer

476

views

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

calculus integration definite-integrals

Aug 2 '15 at 7:15 Community♦ 1

5

10

votes

4

answers

2k

views

Continued fraction for $\tan(nx)$

calculus algebra-precalculus trigonometry continued-fractions

Oct 21 at 15:28 Paramanand Singh 52.1k

4

10

votes

2

answers

297

views

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

abstract-algebra

Apr 16 '17 at 1:46 Xam 4,590

10

votes

1

answer

149

views

Irrationality of $\sum\limits_{n=1}^{\infty} r^{-n^{2}}$ for every integer $r > 1$

irrational-numbers

Mar 19 '17 at 11:59 Sophie 1,602

6

10

votes

1

answer

336

views

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

sequences-and-series number-theory reference-request

Jul 13 '15 at 9:58 Community♦ 1

6

9

votes

1

answer

291

views

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

calculus integration definite-integrals elliptic-integrals

Aug 19 '17 at 10:41 Paramanand Singh 52.1k

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105 Questions

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

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

An infinite series plus a continued fraction by Ramanujan

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

What is the use of hyperreal numbers?

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

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

Taylor's Theorem with Peano's Form of Remainder

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

Proof of a Ramanujan Integral

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

An alternative proof of Cauchy's Mean Value Theorem

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

Bellard's exotic formula for $\pi$

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

Monotone functions and non-vanishing of derivative

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

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

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]

Bi-linear relation between two continued fractions

Continuous decreasing function has a fixed point

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

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

Function satisfying $\lim_{x\to 0}\frac{f(ax)}{f(x)}=a$

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

Continued fraction for $\tan(nx)$

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

Irrationality of $\sum\limits_{n=1}^{\infty} r^{-n^{2}}$ for every integer $r > 1$

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

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