User onepound - Mathematics Stack Exchange

11 votes

2 answers

507 views

What does the !! mean in trigonometric identity?

asked Jan 12, 2020 at 17:23

10 votes

1 answer

308 views

Is there an identity for $\sum_{k=0}^{n-1}\tan^4\left({k\pi\over n}\right)$?

asked Nov 6, 2022 at 20:30

10 votes

1 answer

393 views

Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

asked Jul 16, 2023 at 18:07

9 votes

1 answer

543 views

Is there any identity for $\sum_{k=1}^{n}\tan\left(\theta+\frac{k\pi}{\color{red} {2n+1}}\right)$?

asked Feb 11, 2022 at 14:19

7 votes

2 answers

289 views

Is there an identity for $\sum_{k=0}^{n-1}\csc\left(x+ k \frac{\pi}{n}\right)\csc\left(y+ k \frac{\pi}{n}\right)$?

asked May 8, 2023 at 19:56

4 votes

0 answers

323 views

What are the minor and major arcs in the Circle method (Hardy & Littlewood)?

asked Jan 1, 2019 at 11:39

4 votes

1 answer

120 views

How to solve integral $\int \log (x+\frac{1}{2}-\frac{\arctan(\tan(\pi(x+\frac{1}{2})))}{\pi})dx$?

asked Oct 25, 2019 at 10:40

4 votes

3 answers

2k views

Turning sum to integral representation

asked Dec 19, 2017 at 20:23

3 votes

1 answer

166 views

Algebraic manipulation in Vaughan's book on the circle method

asked Jun 30, 2018 at 19:14

3 votes

1 answer

488 views

Undersanding definition of Riemann-Stieltjes Integral used in Edwards book

asked Oct 13, 2018 at 16:07

3 votes

1 answer

54 views

Trouble understanding steps in convolution

asked Dec 23, 2018 at 11:41

3 votes

1 answer

235 views

Product-to-sum trigonometry identity

asked Jul 20, 2014 at 11:35

3 votes

4 answers

205 views

How to find Sum of Sum of Partial Harmonic Series: $\sum_{b=1}^{m} \sum_{k=1}^{b} \frac{1}{k} $?

asked Jul 16, 2019 at 18:20

3 votes

0 answers

103 views

How can one find an identity for $\sum_{k=0}^{n-1}\tan^2(\frac{k\pi y}{n}) $?

asked Mar 14, 2022 at 18:37

3 votes

1 answer

205 views

How to show that $2\sum_{j=1}^{N}\cot(\frac{\pi j}{2N+1})$ is related to $(\frac{4 \text{N}+2}{\pi}) (H_{\text{N}}+\log (\frac{2}{\pi }))$?

asked Jul 20, 2020 at 12:48

3 votes

2 answers

2k views

modelling smooth square wave function

asked Dec 27, 2020 at 14:00

2 votes

2 answers

250 views

How to prove identity $\sum_{k=0}^{n-1}\tan^2\left(\theta+{k\pi\over n}\right)=n^2\cot^2\left({n\pi\over2}+n\theta\right)+n(n-1)$?

asked Dec 9, 2022 at 23:23

2 votes

1 answer

191 views

How to use contour method with $\int_0^{\pi} \tan (x) \log \left(\cos ^2(x)\right) dx =0$?

asked Jan 8, 2023 at 15:51

2 votes

0 answers

87 views

How to find $\int\log(\cos(a/x))dx$ in closed form or asymptotic estimation?

asked Dec 29, 2019 at 18:43

2 votes

1 answer

334 views

Step by step derivation of Robin's inequality $\sigma(n) < e^\gamma n \log \log n$

asked Mar 20, 2019 at 10:01

2 votes

2 answers

123 views

proof that odd polynomial has root

asked Sep 20, 2014 at 22:30

2 votes

1 answer

64 views

Trouble understanding part of thereom: Every prime congruent 1 mod (4) can be written as sum of two squares.

asked Apr 16, 2016 at 20:36

2 votes

2 answers

131 views

Interpreting big O for Sum of Primes < n

asked Oct 8, 2017 at 17:08

2 votes

1 answer

451 views

Approximation of primorial # in terms of $\pi(x)$

asked Dec 11, 2017 at 15:26

2 votes

1 answer

280 views

Bertrand's Theorem: prime-power decomposition proof

asked Feb 24, 2018 at 12:12

2 votes

1 answer

427 views

help with a simple example of the Hardy-Littlewood circle method.

asked May 26, 2018 at 19:12

1 vote

1 answer

480 views

Using asymptotic expansion of integral

asked Jun 7, 2018 at 12:20

1 vote

1 answer

93 views

Help understanding limits in Ramanujans proof of Bertrand's Postulate

asked Mar 29, 2018 at 9:17

1 vote

0 answers

83 views

Asymptotic expansion of the integral $\int_2^T \frac{\cosh ^{-1}(T-x+2)}{\ln(x)} \, dx$

asked Jan 5, 2018 at 11:00

1 vote

1 answer

445 views

Flip side of Feynman's trick for Integration

asked Jan 12, 2018 at 16:49

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73 Questions

What does the !! mean in trigonometric identity?

Is there an identity for $\sum_{k=0}^{n-1}\tan^4\left({k\pi\over n}\right)$?

Is there an identity for $\sum_{k=0}^{n-1}\csc(w+ k \frac{\pi}{n})\csc(x+ k \frac{\pi}{n})\csc(y+ k \frac{\pi}{n})\csc(z+ k \frac{\pi}{n})$?

Is there any identity for $\sum_{k=1}^{n}\tan\left(\theta+\frac{k\pi}{\color{red} {2n+1}}\right)$?

Is there an identity for $\sum_{k=0}^{n-1}\csc\left(x+ k \frac{\pi}{n}\right)\csc\left(y+ k \frac{\pi}{n}\right)$?

What are the minor and major arcs in the Circle method (Hardy & Littlewood)?

How to solve integral $\int \log (x+\frac{1}{2}-\frac{\arctan(\tan(\pi(x+\frac{1}{2})))}{\pi})dx$?

Turning sum to integral representation

Algebraic manipulation in Vaughan's book on the circle method

Undersanding definition of Riemann-Stieltjes Integral used in Edwards book

Trouble understanding steps in convolution

Product-to-sum trigonometry identity

How to find Sum of Sum of Partial Harmonic Series: $\sum_{b=1}^{m} \sum_{k=1}^{b} \frac{1}{k} $?

How can one find an identity for $\sum_{k=0}^{n-1}\tan^2(\frac{k\pi y}{n}) $?

How to show that $2\sum_{j=1}^{N}\cot(\frac{\pi j}{2N+1})$ is related to $(\frac{4 \text{N}+2}{\pi}) (H_{\text{N}}+\log (\frac{2}{\pi }))$?

modelling smooth square wave function

How to prove identity $\sum_{k=0}^{n-1}\tan^2\left(\theta+{k\pi\over n}\right)=n^2\cot^2\left({n\pi\over2}+n\theta\right)+n(n-1)$?

How to use contour method with $\int_0^{\pi} \tan (x) \log \left(\cos ^2(x)\right) dx =0$?

How to find $\int\log(\cos(a/x))dx$ in closed form or asymptotic estimation?

Step by step derivation of Robin's inequality $\sigma(n) < e^\gamma n \log \log n$

proof that odd polynomial has root

Trouble understanding part of thereom: Every prime congruent 1 mod (4) can be written as sum of two squares.

Interpreting big O for Sum of Primes < n

Approximation of primorial # in terms of $\pi(x)$

Bertrand's Theorem: prime-power decomposition proof

help with a simple example of the Hardy-Littlewood circle method.

Using asymptotic expansion of integral

Help understanding limits in Ramanujans proof of Bertrand's Postulate

Asymptotic expansion of the integral $\int_2^T \frac{\cosh ^{-1}(T-x+2)}{\ln(x)} \, dx$

Flip side of Feynman's trick for Integration