Question

Infinite sum of powerseries likely converges to a powerseries with rational coefficients and has then a simple generating function... proof?

score 112 · Answer 1 · 2021-05-17 10:13:08

112

Views

Infinite sum of powerseries likely converges to a powerseries with rational coefficients and has then a simple generating function... proof?

Published on 17 May 2021 - 10:13

score 418 · Answer 2 · 2021-05-26 22:26:38

418

Views

Square rooting in tetration.

Published on 26 May 2021 - 22:26

score 1k · Answer 3 · 2021-06-10 00:57:56

1k

Views

Integral over domain of infinite tetration of x over extended domain from 0 to $\sqrt[e]e$. Possible $\int_{e^{-e}}^{e^\frac1e} x^{x^{…}}dx$ solution.

Published on 10 Jun 2021 - 0:57

score 148 · Answer 4 · 2021-06-16 14:43:31

148

Views

Alternate non-sum form or integral representation of $\sum_{x\in \Bbb Z} (-1)^x \left(x^\frac1x -1\right)$.

Published on 16 Jun 2021 - 14:43

score 198 · Answer 5 · 2026-03-22 05:02:31

198

Views

Categorification of tetration, is it possible?

Published on 22 Mar 2026 - 5:02

score 233 · Answer 6 · 2021-06-25 02:15:37

233

Views

On $\int \sqrt[x]x$dx. Solution found for $eW\left(\frac1e\right)\le x\le e$.

Published on 25 Jun 2021 - 2:15

score 236 · Answer 7 · 2021-06-30 05:01:24

236

Views

How to evaluate the finite power tower $\tan(1°)^{\tan(2°)^{\tan(3°)^{\cdot^{\cdot^{\cdot^{\tan(44°)^{\tan(45°)}}}}}}}$

Published on 30 Jun 2021 - 5:01

score 372 · Answer 8 · 2021-07-07 02:47:30

372

Views

Is there a better solution for $\mathrm{\int (a^t)^{(a^t)}dt= C+t+\frac1{\,ln(a)}\sum_{n=0}^\infty \frac{(-1)^n Q(n+1,-nt\ln(a))}{n^{n+1}}\,dt}$?

Published on 07 Jul 2021 - 2:47

score 483 · Answer 9 · 2021-07-10 16:41:15

483

Views

Solve $\sum_{n=1}^\inftyΓ(-n,-n)\mathop= \pi\left(\frac1e-1\right)i+ \sum_{n=1}^\infty \frac{(-1)^n \text{Ei}(n)}{n!}+\sum_{n=1}^\infty a_n･(-e)^n $

Published on 10 Jul 2021 - 16:41

score 508 · Answer 10 · 2021-07-12 15:00:14

508

Views

Prove or disprove that the function is convex .

Published on 12 Jul 2021 - 15:00

score 84 · Answer 11 · 2021-07-14 22:36:48

84

Views

Is $\exp(a\exp(a\exp(a\cdots)))$, where $a=\pi/2$, a valid representation of $i$?

Published on 14 Jul 2021 - 22:36

score 220 · Answer 12 · 2021-07-19 13:44:15

220

Views

Solution to the Equation $x^x = 0$.

Published on 19 Jul 2021 - 13:44

score 372 · Answer 13 · 2021-08-01 17:38:23

372

Views

Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Published on 01 Aug 2021 - 17:38

score 434 · Answer 14 · 2026-03-26 16:14:12

434

Views

Integral form(s) of a general tetration/power tower integral solution: $\sum\limits_{n=0}^\infty \frac{(pn+q)^{rn+s}Γ(An+B,Cn+D)}{Γ(an+b,cn+d)}$

Published on 26 Mar 2026 - 16:14

score 15 · Answer 15 · 2026-03-04 02:46:55

15

Views

Repeated Exponentiation doubt

Published on 04 Mar 2026 - 2:46

List Question

Infinite sum of powerseries likely converges to a powerseries with rational coefficients and has then a simple generating function... proof?

Square rooting in tetration.

Integral over domain of infinite tetration of x over extended domain from 0 to $\sqrt[e]e$. Possible $\int_{e^{-e}}^{e^\frac1e} x^{x^{…}}dx$ solution.

Alternate non-sum form or integral representation of $\sum_{x\in \Bbb Z} (-1)^x \left(x^\frac1x -1\right)$.

Categorification of tetration, is it possible?

On $\int \sqrt[x]x$dx. Solution found for $eW\left(\frac1e\right)\le x\le e$.

How to evaluate the finite power tower $\tan(1°)^{\tan(2°)^{\tan(3°)^{\cdot^{\cdot^{\cdot^{\tan(44°)^{\tan(45°)}}}}}}}$

Is there a better solution for $\mathrm{\int (a^t)^{(a^t)}dt= C+t+\frac1{\,ln(a)}\sum_{n=0}^\infty \frac{(-1)^n Q(n+1,-nt\ln(a))}{n^{n+1}}\,dt}$?

Solve $\sum_{n=1}^\inftyΓ(-n,-n)\mathop= \pi\left(\frac1e-1\right)i+ \sum_{n=1}^\infty \frac{(-1)^n \text{Ei}(n)}{n!}+\sum_{n=1}^\infty a_n･(-e)^n $

Prove or disprove that the function is convex .

Is $\exp(a\exp(a\exp(a\cdots)))$, where $a=\pi/2$, a valid representation of $i$?

Solution to the Equation $x^x = 0$.

Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Integral form(s) of a general tetration/power tower integral solution: $\sum\limits_{n=0}^\infty \frac{(pn+q)^{rn+s}Γ(An+B,Cn+D)}{Γ(an+b,cn+d)}$

Repeated Exponentiation doubt

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