3
votes
0answers
214 views

quasi periodic continued fractions and powers of e, tanh, tan

It is well known that some transcendental numbers like e.g. rational multiples of $e^{2/n}$ with $n\in\mathbb N $, when written as regular continued fractions (R.C.F.), yield what can be called a ...
10
votes
5answers
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 ...
16
votes
6answers
3k views

Showing e is transcendental using its continued fraction expansion

Can the transcendence of e be shown using its continued fraction expansion e = [2;1,2,1,1,4,1,1,6,...]?