Question

Can we characterize functions, like exponentials, the gamma function, and tetration, as solutions of an optimization problem?

score 63 · Answer 1 · 2022-04-17 18:54:10

63

Views

Can we characterize functions, like exponentials, the gamma function, and tetration, as solutions of an optimization problem?

Published on 17 Apr 2022 - 18:54

score 258 · Answer 2 · 2022-04-20 21:19:48

258

Views

General formula for the derivative of a pentation?

Published on 20 Apr 2022 - 21:19

score 317 · Answer 3 · 2022-04-28 17:58:39

317

Views

Negative Tetrations?

Published on 28 Apr 2022 - 17:58

score 40 · Answer 4 · 2022-06-30 12:23:58

40

Views

What is $^{y(slog_xa)}x$?

Published on 30 Jun 2022 - 12:23

score 215 · Answer 5 · 2022-07-10 11:37:48

215

Views

Improving the result $\int_0^\infty\frac1{x^x}\, dx<2.$

Published on 10 Jul 2022 - 11:37

score 151 · Answer 6 · 2022-07-11 03:19:03

151

Views

Does $^{\frac12}{a}=$ $\sqrt{a}_s$?

Published on 11 Jul 2022 - 3:19

score 139 · Answer 7 · 2026-03-25 21:51:12

139

Views

Has There Been Any Study of the Quotient-root Derivative Definition $\lim_{\Delta x \to 0} \sqrt[\Delta x]{\frac{f(x + \Delta x)}{f(x)}}$?

Published on 25 Mar 2026 - 21:51

score 152 · Answer 8 · 2022-08-12 17:39:12

152

Views

Convergence value of the unique positive real root of ${^{m + 1}x} = {^{m}x} + 1$ as $m$ approaches infinity

Published on 12 Aug 2022 - 17:39

score 74 · Answer 9 · 2022-09-17 12:44:29

74

Views

Find f(32) given f(x) = f(x-1) + 2^(f(x-1)+1) and f(0) = 5

Published on 17 Sep 2022 - 12:44

score 68 · Answer 10 · 2026-02-24 08:34:28

68

Views

Solving $\frac{d^{n-1}}{da^{n-1}}(f^n(a)g’(a))=h(a,n)(n+u)^{vn},v<0$ from Lagrange reversion

Published on 24 Feb 2026 - 8:34

score 307 · Answer 11 · 2022-09-21 07:28:45

307

Views

Solving an infinite system of equations for the coefficients of a power series for $f(x+1)=\exp(f(x))$

Published on 21 Sep 2022 - 7:28

score 179 · Answer 12 · 2026-03-25 21:46:51

179

Views

Possible Tetration extension for a specific interval (part 1)

Published on 25 Mar 2026 - 21:46

score 574 · Answer 13 · 2022-10-17 12:48:14

574

Views

How to approximate the result of a tetration

Published on 17 Oct 2022 - 12:48

score 188 · Answer 14 · 2022-10-24 10:22:19

188

Views

How to compute tetration of values where the value $k$ is a negative integer?

Published on 24 Oct 2022 - 10:22

score 369 · Answer 15 · 2022-11-04 01:55:45

369

Views

Can the second integral of $x^x$ be expressed in terms of the first integral and standard mathatical functions?

Published on 04 Nov 2022 - 1:55

List Question

Can we characterize functions, like exponentials, the gamma function, and tetration, as solutions of an optimization problem?

General formula for the derivative of a pentation?

Negative Tetrations?

What is $^{y(slog_xa)}x$?

Improving the result $\int_0^\infty\frac1{x^x}\, dx<2.$

Does $^{\frac12}{a}=$ $\sqrt{a}_s$?

Has There Been Any Study of the Quotient-root Derivative Definition $\lim_{\Delta x \to 0} \sqrt[\Delta x]{\frac{f(x + \Delta x)}{f(x)}}$?

Convergence value of the unique positive real root of ${^{m + 1}x} = {^{m}x} + 1$ as $m$ approaches infinity

Find f(32) given f(x) = f(x-1) + 2^(f(x-1)+1) and f(0) = 5

Solving $\frac{d^{n-1}}{da^{n-1}}(f^n(a)g’(a))=h(a,n)(n+u)^{vn},v<0$ from Lagrange reversion

Solving an infinite system of equations for the coefficients of a power series for $f(x+1)=\exp(f(x))$

Possible Tetration extension for a specific interval (part 1)

How to approximate the result of a tetration

How to compute tetration of values where the value $k$ is a negative integer?

Can the second integral of $x^x$ be expressed in terms of the first integral and standard mathatical functions?

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