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  and the theory of continued fractions
1/3] G(q) and G(q) is Ramanujans cubic continued fraction
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
Pearce , Conolly and Langaris , Flajolet and Guillemin , Parthasarathy and Lenin , , , , Parthasarathy and Selvaraju  and Krishnakumar et al  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.