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

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2answers
77 views

Online encyclopedia of maths and physics constants?

The OEIS is amazing, I used to spend hours creating sequences using arbitrary algorithms and look it up to see if it has an alternate definition and what's the meaning and the history of this ...
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1answer
127 views

Sequence with Prime Numbers

I was looking a question in a calculus book which used the following steps to show that following sequence has a limit (called Euler's constant $\gamma$): $$t_n = \sum_{i=1}^n\left(\frac{1}{n}\right) ...
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1answer
76 views

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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1answer
57 views

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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1answer
47 views

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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1answer
92 views

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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0answers
369 views

$\pi^4 + \pi^5 \approx e^6$ is anything special going on here?

Saw it in the news: $$(\pi^4 + \pi^5)^{\Large\frac16} \approx 2.71828180861$$ Is this just pigeon-hole? DISCUSSION: counterfeit $e$ using $\pi$'s Given enough integers and $\pi$'s we can ...
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0answers
83 views

Why does the tribonacci constant have a trilogarithm ladder?

When I came across the dilogarithm ladders of Coxeter and Landen, namely, $$\text{Li}_2(\alpha^6)-4\text{Li}_2(\alpha^3)-3\text{Li}_2(\alpha^2)+6\text{Li}_2(\alpha)-\tfrac{7}{5}\zeta(2)=0\tag1$$ ...
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0answers
76 views

Find a constant $C_p$ that satisfies $|f(x+p)-f(y+p)|\le C_p|f(x)-f(y)|$

Let $B^n$ be the unit open ball in $\mathbb{R}^n$, $p\in \mathbb{R}^n$ and $f\colon \mathbb{R}^n\to B^n$ defined as $f(x)=\frac{1}{1+|x|}x$. I believe there are constants $C_p>0$ such that ...
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0answers
53 views

The $q$-continued fraction for tribonacci constant and others

Let $q = e^{-2\pi}$. We are familiar with Ramanujan's beautiful continued fraction, $$\cfrac{q^{1/5}}{1 + \cfrac{q} {1 + \cfrac{q^2} {1 + \cfrac{q^3} {1+\ddots}}}} = {\sqrt{5+\sqrt{5}\over ...
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0answers
126 views

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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0answers
51 views

Irrationality of $\pi+c$

How to prove that $\pi+c$ is irrational? where $c$ is the Champernowne Constant.
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0answers
62 views

Are there famous complex constants?

Are there any famous constants (like $\pi$ and $e$) that are complex? More specifically, to rule out trivial complex numbers, are there any famous constants of the form $a+bi$ with $a \neq 0 \wedge b ...
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0answers
42 views

Champernowne constant - summation and behavior of terms in continued fraction expansion

Is there an infinite summation that gives the Champernowne constant? Wikipedia has one, and so does Wolfram MathWorld. Are they valid? If so, could someone explain why, i.e how do they work? Also, ...
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0answers
242 views

In the Hunt for Kaprekar's Constants for more than 4 digits.

Kaprekar's constant is $6174$ . Take any four digit number with at least two different digits; create two four digit numbers by writing the digits in descending order and in ascending order; subtract ...
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0answers
50 views

Is $e$ uniformly distributed in all bases?

There has been talk of whether or not $\pi$ is normal, i.e. uniformly distributed in all bases $b$ where $b\ge2$. The general response has been that we expect that it is, and have found no obvious ...
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0answers
18 views

Use of the constant of integration

I have a differential equations question: Given the differential equation $$t(t+1) \frac{ds}{dt} = sln(s)$$ it can be trivially solved to be $$ln ln s = ln(t) - ln(t+1) +C$$ As known, C is the ...
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0answers
42 views

The probabilistic interpretation of ramanujan's constant $ e^{\pi\sqrt{163}}$

Some of the mathematical constant has an interesting probabilistic interpretation. For example, "$\large\pi$". Suppose two integers are chosen at random. What is the probability that they are ...
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0answers
48 views

Has anyone established an upper bound for the least integer $k$ such that infinitely many primes have at most $k$ ones in their binary representation?

Has anyone established an upper bound for the least integer $k$ such that infinitely many primes have at most $k$ ones in their binary representation? $2$ is the only prime with $1$ one, the Fermat ...
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0answers
77 views

Linear second order PDE with constant coefficients

I am doing this mathematical problem $c*G_{vv}+ d*G_{u} + e*G_{v} +f*G=0$, where $c, d, e$ and $f$- are constant coefficients. I already know that this is second order PDE and we classify it by ...
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0answers
99 views

Quartic Polynomial Manipulation

I have a quartic polynomial in $x$ (too long to write here) $f(x,c_1, c_2, c_2)$ where $c_1, c_2, c_3$ are constants which I have complete freedom over how to fix their values, as long as they are ...
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0answers
41 views

Show that $\lim_{n \to \infty} p(n) = 1-\frac{1}{e}$

Let $p(n)$ denote the probability that a randomly chosen one-to-one function $f:\lbrace 1,2,3...,n \rbrace \rightarrow \lbrace 1,2,3...,n \rbrace$ has a least one fixed point. (least one integer $k$ ...
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0answers
15 views

Finding the constant in a joint density function

I have been having a bit of difficulty with the following example, whenever i integrate the terms vanish. Any help is appreciated! The joint density function of X and Y is given by $$f(x , y) = ...
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0answers
26 views

Max n value for $\frac{1}{x^x}=y^y+n$?

I was looking at the graph of $$\frac{1}{x^x}=y^y+n$$ and found that it disappears at n greater than about $0.752$. What is the exact constant definition for n and why does the graph disappear ...
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0answers
34 views

clarity in the solution of the following problem

$$(D^2+D)y=x^2+2x+4$$ I found the solution as $$CF=C_{1}+e^{-x}C_{2}$$ and PI=$$\left(\frac{x^3}{3}\right)+4x$$ but the solution from my teacher is PI = $$\left(\frac{x^3}{3}\right)+4x+C3$$ Where ...
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0answers
17 views

How to find the constant of an expanded binomial expression?

Can somebody please explain how to find the Constant Term in an Expanded Binomial Expression? I have looked online and a lot of the explanations have confused me. The problem i'm currently on is ...
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0answers
44 views

What is he easiest way to approximate γ as a decimal number?

What is the easiest way to give the numerical value of the Euler-Mascheroni constant? The mathmetical way to give that value? Thanks lot!
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0answers
123 views

Calculating Closed form of Basel type problem.

I want to find the sum of $\displaystyle\sum_{n=1}^\infty \frac{1}{n^{\phi(n)}}$. where $\phi$ is Euler's totient. So for example $\frac{1}{1^1} + \frac{1}{2^1} + \frac{1}{3^2} +\frac{1}{4^2} + ...
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0answers
78 views

Is there a name for this constant? (0.0100011011…)

It's the simplest number I could think of that contains any finite binary code in its digits: $$\begin{align} c &= 0.0100011011000001010011100101110111...\\ &= ...
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0answers
53 views

$f$ 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 ...