Re: Classes of transcendental number, continued fractions, diophantine approximations

In article <[EMAIL PROTECTED]>,
Diana <[EMAIL PROTECTED]> wrote:

>I am also interested in the fact that Pi doesn't have a continued fraction
>expansion which is an understandable pattern, but E does. There must be more
>that these two transcendental numbers which have interesting continued
>fraction expansions? I am wondering if the "classes" of transcendental
>numbers are outlined anywhere?

One class of examples is related to Lambert's continued fraction for
tan(z):
tan(1/n) = [0; n-1, 1, 3n-2, 1, 5n-2, 1, 7n-2, 1, ...]
tanh(1/n) = [0; n, 3n, 5n, 7n, ...]

See the sci.math thread "Patterns in continued fractions" from
March 1997. 

Robert Israel                                [EMAIL PROTECTED]
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            
Vancouver, BC, Canada V6T 1Z2