# Tagged Questions

**2**

votes

**1**answer

59 views

### Expressions in “continued” monotone functions

Recall continued fractions: http://en.wikipedia.org/wiki/Continued_fraction
Now take a look at this question: ...

**6**

votes

**0**answers

236 views

### Birth-Death Process associated with Orthogonal Polynomials

I have read in various places the following objects are related:
orthogonal polynomials
birth-death processes
Lattice paths
continued fractions
After a lot of searching online, I found sketches ...

**10**

votes

**5**answers

856 views

### Euler's divergent series sum n!*(-1)^n: what is known about the resulting constant?

Much of the theory of continued fractions has been developped by Euler in the 18th century. The little survey "Euler: continued fractions and divergent series (and Nicholas Bernoulli)", mentions ...

**1**

vote

**1**answer

301 views

### Best rational approximation in a special sense

Let $\alpha$ be an irrational number, $n\geq 1$ and
$ X_n=\lbrace (x,y) \in {\mathbb Z}^2 | |y| \leq n, \ x+y\alpha >0 \rbrace$
Now let $(x_n,y_n)$ minimize the quantity $x+y\alpha$ on $X_n$. ...