Second, in order to be able to express (almost) all the nuclide masses through

continued fractions, we have to split the data set of non-radioactive nuclide masses into groups:

In section 5, we establish some explicit evaluations for the Ramanujan-Gollnitz-Gordon

continued fraction, Ramanujan-Selberg

continued fraction and a

continued fraction of Eisenstein using the values of [h.

A

continued fraction can be obtained by iterating such transformations.

We solve the above equations using

continued fractions methodology.

Instead, the backward direction, or equivalently the associated

continued fraction, should be used.

About the characteristic properties of

continued fractions, it can be found in the references [1] and [2].

Mathematically, two opposite oscillation states are characterized through equal

continued fraction representations, but with the difference that in one case all denominators, the free link and the phase shift have been multiplied by (-1).

He would also like to thank Vladimir Arnold, Elena Korkina and Mark Sapir for teaching him about multidimensional

continued fractions.

n]) > n x K(a); The Fibonacci numbers and the Lucas numbers do not exist in the sequence {K(n)}; Let C be the

continued fraction of the sequence {K(n)}, then C is convergent and 2 < C < 3; K([2.

Ramanujan gave three more related

continued fractions.

An other fractal scaling model was used in a previous article of the present author [9], and a set of 78 accurately measured elementary particle masses was expressed in the form of

continued fractions.

Along with traditional content they include material rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration and

continued fractions.

There is some appeal in looking for

continued fractions which have a simple form.

It is interesting to observe that we are led quite naturally to consider a cyclic version of continuants, as they are usually introduced for

continued fractions (see Graham et al.

continued fractions, Ramanujan formulas, Laplace transform