# Questions tagged [transcendental-functions]

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### How can you prove algebraic inputs of a transcendental function are transcendental?

In general, it's not true that a given transcendental function $f(z)$ will give you a transcendental output for countably infinite algebraic inputs, but is there a condition that can prove that ...
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### What is transcendental equation/function?

I looked up several sources on the internet. A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for. Such equations often do not have ...
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### Does this transcendental equation have solutions for a non real variable?

Having solved the transcendental equation $e^{\frac{1}{\log(x)}}=x$ I found that it has solutions for a real variable $x.$ Does it have solutions for not real $x$ (i.e. over the quaternions, octonions)...
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### Transcendence of $x^x = p \in \mathbb{P}$

I'm going straight for the question, so: let $x^x = p \in \mathbb{P}$, then $x$ is irrational. The proof is obvious, $p \neq a^a$ for some integer $a$, so $x^x = (\frac{a}{b})^{\frac{a}{b}}$, suppose ...
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### how to solve $A\ln(1+t)-A\frac{t}{1+t} + B\frac{\ln^2(1+t)}{t^2}=0$

Does anyone have any ideas on how to solve $t$ on $A\ln(1+t)-A\frac{t}{1+t} + B\frac{\ln^2(1+t)}{t^2}=0$, where $A$ and $B$ are constants. It seems impossible to solve such an complex function. Is ...
### how to solve a $\log(1+\frac1x)*x$ function
I know lambert function is available to solve function like $xln(x)$, I wonder if there is a similar way I can solve function $b - x log_2(1+\frac{a}{x})=0$.