# Tagged Questions

For questions about mathematical constants, that are "significantly interesting in some way".

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### What is the algebraic role of the mathematical constant $\gamma$?

Mathematical constants $\pi$, $e$, $i$ have a lot of algebraic roles. They appear as identity elements, idempotents, invariant elements etc against various operations and sets. This is illustrated by ...
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### Terms that cannot be solved for a variable

Yesterday our analysis professor told us you cannot solve $$y = e^x+2/(1+x^2)$$ for x, but you have the option to approximate this numerically. He did not prove that, he just noted it. I can't ...
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### calculating the position of a given digit in a constant (e.g. $\pi$)

I'm aware that there are a lot BBP type formulas out there which extract the n-th digit of the observed constant. I'm asking for the reverse action, namely, is it possible to find the first ...
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### Finding Constants on a Differential Equation

Question (from my sample exercises in calculus): Find constants $A, B$ and $C$ such that the function $$y=A\sin x+B\cos x$$ satisfies the differential equation $$y''+y'-2y=\sin x.$$ I am ...
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### What denotes the essence of a function object in mathematics?

In other words, when does something become a function, and why? Take this, for example: x = y (x + z) = 350 Is anything enclosed within the brackets considered ...
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### The Tribonacci constant and the Dragon

Let $x = \frac{\ln T}{\ln 2} = 0.879146\dots$ where $T$ is the tribonacci constant, then x solves the transcendental equation, $$4^x(2^x-1)=(2^x+1)$$ Let $x = \frac{\ln y}{\ln 2} = 1.523627\dots$ ...
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### $f$ is analytic with range as a circle

I was given that range of $f$ lies on a cirlce, and $f$ is analytic on $D$. I want to show that $f$ is constant. This is my approach: I suppose that $f$ lies on a circle $|w-P|=R$, where $P,R$ are ...