This, together with the fact that well-approximations come from the

continued fraction, allows us to arrive at our desired estimate.

The celebrated Rogers-Ramanujan

continued fraction and its product representation is

infinity]]-theory [7] and the theory of

continued fractions [8].

1/3] G(q) and G(q) is Ramanujans cubic

continued fraction defined by

In order to decompose into a

continued fraction, for example, the function ([D.

This

continued fraction is finite if and only if [alpha] [member of] K(X).

e]) and S is the

continued fraction (e is Euler's number)

At the first step it is necessary to subject the characteristics (3) to synthesis by using the method of distribution on a

continued fraction (used for the first time to synthesize electrical circuits - the Cauer method).

It remains only to show that the

continued fraction in the right-hand side of (19) satisfies the same functional equation, which is done in a separate lemma below.

There are many consequences of this

continued fraction theorem, e.

Pearce [18], Conolly and Langaris [4], Flajolet and Guillemin [7], Parthasarathy and Lenin [13], [14], [15], [17], Parthasarathy and Selvaraju [16] and Krishnakumar et al [19] have applied

continued fraction technique to study the transient behavior of the stochastic systems.

Instead, the backward direction, or equivalently the associated

continued fraction, should be used.

Such an expression is called a

continued fraction, and we denote it by <[x.

1 can be used to evaluate the Ramanujan's cubic

continued fraction.

The program's advanced math capabilities include optimized algorithms for statistical computation, numericalization of root objects,

continued fraction improvements, evaluation of roots for polynomials with algebraic number coefficients, and implementation of GCD by Chinese remainders.