🚀 go-pugleaf

Can anyone recommend a web site where there is some discussion in depth
of "special"
continued fractions?  By this term, I refer to continued fractions
representing numbers OTHER than quadratic surds (and therefore
non-periodic), yet displaying some type of predictable pattern.  The
simplest example that comes to mind is the simple continued
fraction 1+1/(2+1/(3+1/(4+..., which is a ratio of modified Bessel
functions.  The
continued fractions I am interested in need not be simple ones ; for
example, Ramanujan's continued fraction would qualify.  I am very
interested in studying these types of continued fractions and would like
to know how to derive such expressions and to see a collection of such
results.  Thank you in advance.  Paul Bruckman

From news@news.missouri.edu  Thu Aug 20 10:39:19 1998
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From: Don Steiger <dons@hamilton.math.missouri.edu>
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Subject: Evolution operator for the classical Hamiltonian system.
Date: Thu, 20 Aug 1998 12:38:18 -0500
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Status: RO

Let H(p,q) be a classical Hamiltonian Operator, where p and q represent
position and velocity.  let [ , ] represent the Poisson bracket.  The
differential equations of motion can then be written in terms of the
(closed unbounded) operator L = -[H(), ]:

                        d(p,q)/dt = L((p,q)).

I have seen several articles (in non math journals) that claim that the
solution to the above is exp[tL].  For several reasons, I suspect that
this is only a solution in the strictly formal sense.  The most
immediate reason being that if it were an actual solution then it
would be a solution to the n-body problem.  Anybody have any thoughts on
the subject?
-- 
Don Steiger
dons@hamilton.math.missouri.edu