# Questions tagged [constants]

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

555 questions
Filter by
Sorted by
Tagged with
106 views

1 vote
53 views

### real numbers, constant symbols in first order logic

I have this exercise in my book on first order logic: Let's work out a language for elementary trigonometry. To get you started, let us suggest that you start off with lots of constant symbols- one ...
58 views

### Declaring constants in Sagemath

I want to find the Groebner base of a ideal,the ideal is generated by some polynomials with constant coefficients, but they do not have numerical values. ...
41 views

### Identities with symmetric constants $d_{abc}$ of $SU(N)$

I am searching for some $SU(N)$ identities to help simplify an expression built out of many of the totally-symmetric constants of $SU(N)$, defined as $d_{abc}=2{\rm Tr}[(T^aT^b+T^bT^a)T^c]$. The ...
23 views

### Can we showed the existence of $a_i,b_i$ such that $\zeta(3)(2C-1)=1+\sum_{i=1}^{\infty}(-1)^{b_i}(\zeta(a_i)-1)$

It's a follow up of Show that : $\frac{1}{\zeta(3)}<2C-1$ I showed by hand that : $$\frac{1}{\zeta(3)}<2C-1$$ Using classical continued fraction . Now I want to go further and a conjecture : ...
463 views

### Show that : $\frac{1}{\zeta(3)}<2C-1$

Problem : Show that : $$\frac{1}{\zeta(3)}<2C-1$$ Where we can see the zeta function and the Catalan's constant . It recall me the Faulhaber problem which relate the case $n=1,3$ with a square . ...
13 views

### Algorithm trial error for two value $x,y$ roots .

The motivation was to find a path to evaluate the miminum of the factorial for $x>0$. To start I introduce the equation $ax=x!$ a good value is $a=2$ .The second idea is to introduce the inversed ...
26 views

125 views

### What is $\lim_{x\to \infty}f(x)=\lim_{x\to \infty}\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1$

Working on the Gamma function I found the following: Let $$f(x)=\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1.$$ What is the limit $$\lim_{x\to \infty}f(x)=\,?$$ As possible guess it's ...
109 views

### Catalan's constant unexpected closeness

These days I usually wander around on WolframAlpha to experiment and discover many trivial but curious calculations or mathematical relations. Recently, I have randomly discovered a strange closeness ...
93 views

82 views

### Conjecture about the minimum of the Gamma function

Problem/Conjecture: Let the function : $$f(x)=\frac{((x+x_{\min})!-(x_{\min})!)^{\frac{1}{x}}}{x^{\frac{1}{x^2}}}$$ Where $x_\min$ denotes the minimum abscissa of the Gamma function near by $0.4616$ ...
121 views

98 views

### Prove $f(z) = cz$ for all complex numbers and some $c$

Suppose $f$ is entire and $|f(z)|\geqslant |z|$ $\forall z \in \mathbb{C}$, prove there exists $c \in \mathbb{C}$ such that $f(z) = cz$ $\forall z \in \mathbb{C}$. I want to use Liouville’s theorem ...
86 views

### Finger's Constant

A fingers'constant is defined as to have as first decimal : $$1.2345...$$ I ask for the most emblematic example . For example : $$2-\prod_{k=1}^{\infty}\left(1-\frac{1}{\left(k+1\right)e^{k}}\right)$$ ...
462 views

### Show that $\int_{0}^{\infty}x^{-x}dx<\pi-\ln\pi$

I ask for an inequality which is a follow up of this question: Prove that $\int_0^\infty\frac1{x^x}\, dx<2$ : $$\int_{0}^{\infty}x^{-x}dx<\pi-\ln\pi$$ You can find a nice proof @RiverLi among ...
183 views

165 views

### Why do I get this value?

Can somebody explain this? Why does this happen? Yesterday I was on a popular chat bot and I asked it to make me a code to generate a sequence of numbers. What I wanted, was a script that given a ...
1 vote
309 views

### How to find the constant $C$ such that $f(x)\geq Cx$

Problem : Define for strictly positive $x$ : $$f\left(x\right)=\left(\prod_{k=1}^{\operatorname{floor}\left(x\right)}\left(1+\sum_{n=1}^{k}\frac{1}{k\cdot2^{n}}\right)\right)$$ Does there exists a ...
26 views

### How many significant figures should constants be used to in a calculation where other values are given to varying significant figures?

I was recently helping someone study and review the results of a homework assessment in which physics calculations were being performed. The question was related to calculating planetary core pressure ...
135 views

187 views

### What are the odds that De Vries' formula for the fine structure constant $\alpha$ is a numerical coincidence?

The dimensionless fine structure constant $\alpha \approx \frac1{137}$ has intrigued physicists for over a century. Whilst not currently a majority view, there is a school of thought that considers ...
### Show by hand the inequality $\frac{1}{2\ln2}\left(1-\sqrt{\frac{1-\ln2}{1+\ln2}}\right)>\sqrt{2}-1$
Problem : Show that : $$\frac{1}{2\ln2}\left(1-\sqrt{\frac{1-\ln2}{1+\ln2}}\right)>\sqrt{2}-1$$ Using some approximation using itself algoritm found here (https://en.wikipedia.org/wiki/...