User Nikos Bagis

18 votes

Accepted

A conjectured continued fraction for $\phi^\phi$

answered Apr 16, 2017 at 23:36

11 votes

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Is it true that $\int_0^1 \big(K(k^{1/2})\big)^2\,dk = \frac{7}2\zeta(3)$?

answered Feb 21, 2019 at 0:48

10 votes

Functional analysis proof of Ramanujan's Master Theorem

answered Nov 8, 2018 at 12:51

9 votes

Accepted

$|\log (1 + z)| \leq 2 |z|$ Complex inequality

answered Feb 25, 2018 at 4:28

8 votes

Evaluate improper integral

answered May 27, 2018 at 12:27

8 votes

The most complex formula for the golden ratio $\varphi$ that I have ever seen. How was it achieved?

answered May 20, 2020 at 5:08

7 votes

An infinite series plus a continued fraction by Ramanujan

answered Nov 8, 2016 at 14:23

7 votes

Accepted

a new continued fraction for $\sqrt{2}$

answered May 2, 2017 at 10:27

7 votes

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

answered Jul 22, 2021 at 22:44

6 votes

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

answered Mar 1, 2020 at 7:07

6 votes

Closed form for this integral $\int_{0}^{\infty}\frac{dx}{\sqrt{x}}\, e^{-x^{2}-\frac{b^{2}}{x}}$

answered Nov 7, 2016 at 13:54

6 votes

What is the exact value of $\eta(6i)$?

answered May 2, 2017 at 16:26

6 votes

A closed form of $\sum_{k=1}^\infty \psi^{(1)} (k+a)\psi^{(1)} (k+b)$?

answered Nov 24, 2018 at 23:36

6 votes

Accepted

How to solve this integral/better way to approach?

answered Nov 30, 2018 at 15:54

5 votes

Accepted

This formula is on Wolfram Mathworld but I cannot find it anywhere else online?

answered Jun 30, 2018 at 15:09

5 votes

Is it possible to manipulate Niven's proof of the irrationality of $\pi$ to prove the irrationality of $\sqrt{2}$?

answered Mar 10, 2020 at 22:25

5 votes

Relationship between Stokes's theorem and the Gauss-Bonnet theorem

answered Sep 14, 2019 at 13:29

5 votes

Ramanujan theta function and its continued fraction

answered Apr 19, 2017 at 12:16

5 votes

Rogers-Ramanujan continued fraction in terms of Jacobi theta functions?

answered Oct 28, 2016 at 20:14

5 votes

When is an infinite product of natural numbers regularizable?

answered Nov 6, 2016 at 17:05

5 votes

Accepted

A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.

answered May 14, 2020 at 18:27

5 votes

Accepted

How to solve this system of ODEs

answered May 22, 2020 at 19:10

4 votes

How to go from $\frac{\|g_{k+1}\|}{\|g_{k}\|^2} \leq c$ to $\frac{\|x_{k+1} - x_\|}{\|x_{k} - x_\|^2} \leq c$ as $k\to \infty$

answered Jun 24, 2022 at 17:33

4 votes

Accepted

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

answered May 16, 2020 at 1:32

4 votes

Show that $3x^4+4y^4=19z^4$ has no integer solution

answered Oct 4, 2019 at 15:14

4 votes

Third order nonlinear ODE

answered Feb 6, 2020 at 5:56

4 votes

What is the derivative of Rogers-Ramanujan Continued Fraction?

answered Mar 12, 2017 at 13:51

4 votes

Calculating in closed form $\int _0^1\int _0^1\frac{1}{1+x y (x+y)} \ dx \ dy$

answered May 22, 2018 at 0:52

4 votes

Integral $\int_0^\infty\frac{\ln\left(\sqrt{x+1\vphantom{x^0}}-1\right)\,\ln\left(\sqrt{x^{-1}+1}+1\right)}{(x+1)^{3/2}}dx$

answered Dec 29, 2019 at 13:40

4 votes

Examples of transcendental functions giving almost integers

answered Mar 7, 2019 at 16:18

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148 Answers

A conjectured continued fraction for $\phi^\phi$

Is it true that $\int_0^1 \big(K(k^{1/2})\big)^2\,dk = \frac{7}2\zeta(3)$?

Functional analysis proof of Ramanujan's Master Theorem

$|\log (1 + z)| \leq 2 |z|$ Complex inequality

Evaluate improper integral

The most complex formula for the golden ratio $\varphi$ that I have ever seen. How was it achieved?

An infinite series plus a continued fraction by Ramanujan

a new continued fraction for $\sqrt{2}$

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

On proving that $\sum\limits_{n=1}^\infty \frac{n^{13}}{e^{2\pi n}-1}=\frac 1{24}$

Closed form for this integral $\int_{0}^{\infty}\frac{dx}{\sqrt{x}}\, e^{-x^{2}-\frac{b^{2}}{x}}$

What is the exact value of $\eta(6i)$?

A closed form of $\sum_{k=1}^\infty \psi^{(1)} (k+a)\psi^{(1)} (k+b)$?

How to solve this integral/better way to approach?

This formula is on Wolfram Mathworld but I cannot find it anywhere else online?

Is it possible to manipulate Niven's proof of the irrationality of $\pi$ to prove the irrationality of $\sqrt{2}$?

Relationship between Stokes's theorem and the Gauss-Bonnet theorem

Ramanujan theta function and its continued fraction

Rogers-Ramanujan continued fraction in terms of Jacobi theta functions?

When is an infinite product of natural numbers regularizable?

A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.

How to solve this system of ODEs

How to go from $\frac{\|g_{k+1}\|}{\|g_{k}\|^2} \leq c$ to $\frac{\|x_{k+1} - x_\|}{\|x_{k} - x_\|^2} \leq c$ as $k\to \infty$

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

Show that $3x^4+4y^4=19z^4$ has no integer solution

Third order nonlinear ODE

What is the derivative of Rogers-Ramanujan Continued Fraction?

Calculating in closed form $\int _0^1\int _0^1\frac{1}{1+x y (x+y)} \ dx \ dy$

Integral $\int_0^\infty\frac{\ln\left(\sqrt{x+1\vphantom{x^0}}-1\right)\,\ln\left(\sqrt{x^{-1}+1}+1\right)}{(x+1)^{3/2}}dx$

Examples of transcendental functions giving almost integers