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

learn more… | top users | synonyms

2
votes
1answer
80 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 ...
2
votes
1answer
61 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 ...
1
vote
1answer
51 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 ...
0
votes
1answer
26 views

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 ...
0
votes
1answer
95 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 ...
10
votes
0answers
170 views

Are my calculations of a new constant similar to Mill's constant based on $\lfloor A^{2^{n}}\rfloor$ and Bertrand's postulate correct?

As Wikipedia explains in number theory, Mills' constant is defined as: "The smallest positive real number $A$ such that the floor function of the double exponential function $\lfloor A^{3^{n}}\...
6
votes
0answers
89 views

Why does the tribonacci constant have a trilogarithm ladder?

When I came across the dilogarithm ladders of Coxeter and Landen, namely, $$\text{Li}_2(\alpha^6)-4\text{Li}_2(\alpha^3)-3\text{Li}_2(\alpha^2)+6\text{Li}_2(\alpha)-\tfrac{7}{5}\zeta(2)=0\tag1$$ $$\...
5
votes
0answers
67 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 2}-{1+\...
4
votes
0answers
85 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 $|f(x+p)...
4
votes
0answers
131 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 $x = \frac{\ln y}{\ln 2} = 1.523627\dots$ ...
3
votes
0answers
58 views

A function can provide the complete set of Euler primes via a Mill's-like constant. Is it useful or just a curiosity?

The following $f(m,n)$ function provides the complete set of Euler primes (OEIS A196230): $$f(m,n)=m^2-m+[\lfloor E^{2^n} \rfloor - {\lfloor E^{2^{n-1}} \rfloor}^2 +\frac{\lvert n-(\frac{1}{2}) \...
2
votes
0answers
28 views

Is a possible use of a Mill's constant the encapsulation/encryption of messages?

I wonder if the way that Mill's constant is defined could provide a good data encapsulation and encryption method if instead of encapsulating primes, for instance a simple ASCII message is ...
2
votes
0answers
49 views

Why only a handful of distinct mathematical constants appears in most applications?

Is there some theoretical reasoning behind the fact that the same numbers ($\pi$, $e$, $\gamma$, etc) appear again and again in every application in every field of Mathematics? Most people just ...
2
votes
0answers
56 views

Irrationality of $\pi+c$

How to prove that $\pi+c$ is irrational? where $c$ is the Champernowne Constant.
2
votes
0answers
72 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 ...
2
votes
0answers
46 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, ...
2
votes
0answers
298 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 ...
2
votes
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 ...
1
vote
0answers
44 views

Why do we care about the Champernowne constant?

I was browsing code golf and I came across this challenge: http://codegolf.stackexchange.com/questions/68685/the-rien-number It caught my interest and I wanted to learn a bit more about the ...
1
vote
0answers
21 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 ...
1
vote
0answers
49 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 ...
1
vote
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 ...
1
vote
0answers
94 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 ...
1
vote
0answers
123 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 ...
0
votes
0answers
20 views

Universal Parabolic Constant

I recently learned of a constant that arises in parabolas, similar to that of $\pi$ for circles. Like $\pi$ being the ratio of the circumference of the circle to its diameter, this constant $\sqrt2+\...
0
votes
0answers
43 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 $k$ ...
0
votes
0answers
25 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 $$f(x , y) = $$\...
0
votes
0answers
30 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 (...
0
votes
0answers
35 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 ...
0
votes
0answers
23 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 ...
0
votes
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!
0
votes
0answers
127 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} + \...
0
votes
0answers
86 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...\\ &= 0.\;0\;1\;00\;01\;10\;11\;000\;...
0
votes
0answers
55 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 ...