# Questions tagged [constants]

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

490 questions
Filter by
Sorted by
Tagged with
81 views

### how to prove this identity $s = 2 \int_{- \pi}^{\pi} | \frac{\sin (t) - i}{(\sin (t) + i)^2} | dt = 2 K (- 1) = 2.62206...$

How can we prove this identity? Which, btw, Mathematica know how to simplify so it is missing some fundamental identity (related to the lemniscate constant.) \begin{equation} s = 2 \int_{- \pi}^{\pi}...
1 vote
175 views

59 views

1 vote
96 views

1 vote
61 views

### What does it mean to say "the inequality is tight up to constant factors"?

On the Wikipedia page for Pinsker's inequality, it states "the inequality is tight up to constant factors". $$\delta(P, Q) \leq \sqrt{\frac 1 2 D_\text{KL}(P||Q)}$$ What does this mean? ...
22 views

### Mean value theorem question - proving F constant - answer check

The question: Given $f$ continuity at $[a,b]$ and derivative at $(a,b)$. It is known $f'(x)=0$ for each x belongs to $(a,b)$. prove $f$ is constant. My Answer: Need to prove $f(x)=k$ for each X ... 39 views

### PDEs With Partial Derivatives W.R.T. a Single Variable

Is it always correct to solve partial differential equations as though they were ordinary differential equations if the partial derivatives are only taken with respect to a single variable, even if ...
218 views

### Find extrema of $y=?(x)-x$ with the Minkowski Question Mark function

The Goal: is to figure out the global extrema of the Minkowski Question Mark function $?(x)$. Here is the graph of: $$?(x)-x:$$ The $y$ value of the global maximum was found by systematically ...
20 views

### Solving a PDE Via the Similarity Method Versus Another Method

The PDE is $$u_{xx} + 2u_{tt} = 0$$ I imagine that the solution will be $u(v(x,\ t))$, where $v(x,\ t) = \frac{t}{x}$. So plugging this form into the PDE and using the multivariable chain rule yields ...