Question

Is $\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^n+1}$a complex number? What is happening?

score 140 · Answer 1 · 2022-01-15 13:43:32

140

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Is $\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^n+1}$a complex number? What is happening?

Published on 15 Jan 2022 - 13:43

score 107 · Answer 2 · 2022-02-13 23:22:18

107

Views

Bound this integral $\displaystyle\int_0^\infty \frac{(1-p+pe^{-t})^n -e^{-npt} -(1-p)^n(1-e^{-nt})}{1-e^{-t}}dt$

Published on 13 Feb 2022 - 23:22

score 86 · Answer 3 · 2022-03-31 13:30:42

86

Views

Show the limit $\lim_{\delta \to 0}\int_{\ln(1+\delta)}^{\delta} \frac{e^{-x}}{x}\,dx \to 0 $ in a proof of the Digamma function

Published on 31 Mar 2022 - 13:30

score 215 · Answer 4 · 2022-04-18 04:27:13

215

Views

Switching the sum and integral

Published on 18 Apr 2022 - 4:27

score 212 · Answer 5 · 2022-05-05 13:34:00

212

Views

Derivation of Digamma function

Published on 05 May 2022 - 13:34

score 86 · Answer 6 · 2026-03-25 20:41:22

86

Views

Computing solutions to polygamma function of order 1?

Published on 25 Mar 2026 - 20:41

score 158 · Answer 7 · 2022-05-31 07:00:22

158

Views

Prove $(n-1)! + 1 = n^2$ has only one integer solution

Published on 31 May 2022 - 7:00

score 78 · Answer 8 · 2022-08-03 04:39:42

78

Views

Finding $\sum_{n=0}^{\infty} (-1)^n\left(\frac{1}{(3n+2)^2}-\frac{1}{(3n+1)^2}\right)$

Published on 03 Aug 2022 - 4:39

score 28 · Answer 9 · 2022-10-21 07:47:56

28

Views

Find reference about expansion of gamma function

Published on 21 Oct 2022 - 7:47

score 171 · Answer 10 · 2022-10-27 03:23:18

171

Views

Do we have a closed form for $\int_0^{\infty} \frac{\ln t}{\left(1+t^2\right)^n} d t $?

Published on 27 Oct 2022 - 3:23

score 373 · Answer 11 · 2022-11-15 11:02:30

373

Views

Seeking for other methods to evaluate $\int_0^{\infty} \frac{\ln \left(x^n+1\right)}{x^n+1} dx$ for $n\geq 2$.

Published on 15 Nov 2022 - 11:02

score 163 · Answer 12 · 2022-12-06 15:27:15

163

Views

What will be this limit? I'm having a hard time finding this....

Published on 06 Dec 2022 - 15:27

score 106 · Answer 13 · 2023-01-08 14:30:04

106

Views

Gauss's Digamma Theorem generalization

Published on 08 Jan 2023 - 14:30

score 321 · Answer 14 · 2023-01-08 22:17:56

321

Views

How to prove $\sum_{k=1}^n{n\choose k}\frac{(-1)^{k+1}}{k}=\sum_{k=1}^n\frac{1}{k}$?

Published on 08 Jan 2023 - 22:17

score 162 · Answer 15 · 2023-01-18 13:28:22

162

Views

Inverse of difference of two digamma functions

Published on 18 Jan 2023 - 13:28

List Question

Is $\displaystyle\sum_{n=1}^{\infty} \frac{1}{2^n+1}$a complex number? What is happening?

Bound this integral $\displaystyle\int_0^\infty \frac{(1-p+pe^{-t})^n -e^{-npt} -(1-p)^n(1-e^{-nt})}{1-e^{-t}}dt$

Show the limit $\lim_{\delta \to 0}\int_{\ln(1+\delta)}^{\delta} \frac{e^{-x}}{x}\,dx \to 0 $ in a proof of the Digamma function

Switching the sum and integral

Derivation of Digamma function

Computing solutions to polygamma function of order 1?

Prove $(n-1)! + 1 = n^2$ has only one integer solution

Finding $\sum_{n=0}^{\infty} (-1)^n\left(\frac{1}{(3n+2)^2}-\frac{1}{(3n+1)^2}\right)$

Find reference about expansion of gamma function

Do we have a closed form for $\int_0^{\infty} \frac{\ln t}{\left(1+t^2\right)^n} d t $?

Seeking for other methods to evaluate $\int_0^{\infty} \frac{\ln \left(x^n+1\right)}{x^n+1} dx$ for $n\geq 2$.

What will be this limit? I'm having a hard time finding this....

Gauss's Digamma Theorem generalization

How to prove $\sum_{k=1}^n{n\choose k}\frac{(-1)^{k+1}}{k}=\sum_{k=1}^n\frac{1}{k}$?

Inverse of difference of two digamma functions

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