Question

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

score 500 · Answer 1 · 2021-07-07 15:46:26

500

Views

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

Published on 07 Jul 2021 - 15:46

score 509 · Answer 2 · 2026-03-27 17:04:56

509

Views

Prove or disprove that the function is convex .

Published on 27 Mar 2026 - 17:04

score 221 · Answer 3 · 2026-03-27 17:04:57

221

Views

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

Published on 27 Mar 2026 - 17:04

score 373 · Answer 4 · 2026-03-27 17:04:56

373

Views

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

Published on 27 Mar 2026 - 17:04

score 89 · Answer 5 · 2021-08-04 03:23:07

89

Views

Is there any formula to sum the series $\sum_{k=1}^n{2^{k^k}}$

Published on 04 Aug 2021 - 3:23

score 434 · Answer 6 · 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 412 · Answer 7 · 2021-09-13 02:32:05

412

Views

Can $\int\limits_0^\infty e^{ix^ x}dx$ be written without a limit?

Published on 13 Sep 2021 - 2:32

score 124 · Answer 8 · 2021-09-26 16:33:52

124

Views

About the inequality $f(-x)<\left(\Gamma(1-x)\right)^{\frac{1}{1-x}}$

Published on 26 Sep 2021 - 16:33

score 199 · Answer 9 · 2026-03-27 18:49:42

199

Views

Could someone explain why $\sum_{\substack{a_1,\ldots,a_n\in\mathbb{N}_0\\a_1+\cdots+a_n=n}}\frac{n!}{a_1!\cdots a_n!}=n^n$?

Published on 27 Mar 2026 - 18:49

score 146 · Answer 10 · 2026-03-25 20:20:28

146

Views

Evaluating negative infinite tetration: $\lim\limits_{n\to-\infty}\,^n x=\lim_{n\to\infty}\underbrace{\log_x\left(…\log_x(0)\right)}_n=\,^{-\infty} x$

Published on 25 Mar 2026 - 20:20

score 121 · Answer 11 · 2026-03-27 18:57:08

121

Views

Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Published on 27 Mar 2026 - 18:57

score 1.6k · Answer 12 · 2022-02-15 17:52:03

1.6k

Views

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

Published on 15 Feb 2022 - 17:52

score 94 · Answer 13 · 2022-04-26 14:40:49

94

Views

$f(n)=$, for even integer’s $n$, $\lim_{n\to\infty} \int_{0}^{\infty} \frac{e^x}{^nx} dx$

Published on 26 Apr 2022 - 14:40

score 146 · Answer 14 · 2026-03-25 08:13:43

146

Views

Correct my sketch of proof about the convexity of the "natural" power tower on $[1,\infty)$

Published on 25 Mar 2026 - 8:13

score 41 · Answer 15 · 2022-05-19 07:20:13

41

Views

Digits tower power iterate

Published on 19 May 2022 - 7:20

List Question

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

Prove or disprove that the function is convex .

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

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

Is there any formula to sum the series $\sum_{k=1}^n{2^{k^k}}$

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

Can $\int\limits_0^\infty e^{ix^ x}dx$ be written without a limit?

About the inequality $f(-x)<\left(\Gamma(1-x)\right)^{\frac{1}{1-x}}$

Could someone explain why $\sum_{\substack{a_1,\ldots,a_n\in\mathbb{N}_0\\a_1+\cdots+a_n=n}}\frac{n!}{a_1!\cdots a_n!}=n^n$?

Evaluating negative infinite tetration: $\lim\limits_{n\to-\infty}\,^n x=\lim_{n\to\infty}\underbrace{\log_x\left(…\log_x(0)\right)}_n=\,^{-\infty} x$

Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

$f(n)=$, for even integer’s $n$, $\lim_{n\to\infty} \int_{0}^{\infty} \frac{e^x}{^nx} dx$

Correct my sketch of proof about the convexity of the "natural" power tower on $[1,\infty)$

Digits tower power iterate

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