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15
109
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How to solve $ax^x+bx+c=0$?

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#tetration #discriminant #hyperoperation
173
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Why is $\underbrace {i^{i^{i^{.^{.^{.^{i}}}}}}}_{n \ times}$ converging?

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#sequences-and-series #complex-numbers #tetration
1k
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Is there a Tetration Function?

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#exponentiation #tetration
95
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$w =\operatorname{arcsinh}(1+2\operatorname{arcsinh}(1+2^2\operatorname{arcsinh}(1+2^{2^2}\operatorname{arcsinh}(1+\dotsm$

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#dynamical-systems #hyperbolic-functions #divergence-operator #tetration #nonlinear-dynamics
144
Views

$f(x) = \sqrt x^{{\sqrt[3]{x}}^{\sqrt[4]{x},\cdots}}$ asymptotic?

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#asymptotics #radicals #tetration #power-towers
505
Views

What is $\underbrace{2018^{2018^{2018^{\mathstrut^{.^{.^{.^{2018}}}}}}}}_{p\,\text{times}}\pmod p$ where $p$ is an odd prime?

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#elementary-number-theory #prime-numbers #modular-arithmetic #tetration #big-numbers
70
Views

iterative solution of $x^x=a$

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#sequences-and-series #tetration
112
Views

What is the value of $i^{i^{i^{\cdots}}}$

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#complex-analysis #analysis #tetration
163
Views

Finding a function satisfies $\ln F(x+1)=a F(x)$

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#calculus #sequences-and-series #functional-equations #tetration
105
Views

$f(exp(z)) = f(z) \cdot g(z) $ with closed form solutions?

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#complex-analysis #closed-form #tetration
123
Views

tetration as an iterative solution for the transcendental equation $\sqrt[x]{x}=y$

Published on
#real-analysis #fixed-point-theorems #tetration
191
Views

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

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#elementary-number-theory #modular-arithmetic #arithmetic-functions #tetration #big-numbers
939
Views

What does $ ^3 3$ mean?

Published on
#notation #tetration
570
Views

Area under the infinite tetration curve

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#definite-integrals #lambert-w #tetration #power-towers
646
Views

Is there an exact value to the minimum of the infinite tetration of $x$?

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#convergence-divergence #recreational-mathematics #maxima-minima #tetration

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