contfracinit

Function: contfracinit
Section: sums
C-Name: contfracinit
Prototype: GD-1,L,
Help: contfracinit(M,{lim = -1}): given M representing the power
 series S = sum_{n>=0} M[n+1]z^n, transform it into a continued fraction
 suitable for evaluation.
Doc: Given $M$ representing the power series $S=\sum_{n\ge0} M[n+1]z^n$,
 transform it into a continued fraction in Euler form, using the
 quotient-difference algorithm; restrict to
 $n\leq \kbd{lim}$ if latter is nonnegative. $M$ can be a vector, a power
 series, a polynomial; if the limiting parameter \kbd{lim} is present, a
 rational function is also allowed (and converted to a power series of that
 accuracy).

 The result is a 2-component vector $[A,B]$ such that
 $S = M[1] / (1+A[1]z+B[1]z^2/(1+A[2]z+B[2]z^2/(1+\dots 1/(1+A[lim/2]z))))$.
 Does not work if any coefficient of $M$ vanishes, nor for series for
 which certain partial denominators vanish.
Variant: Also available is
 \fun{GEN}{quodif}{GEN M, long n}
 which returns the standard continued fraction, as a vector $C$ such that
 $S = c[1] / (1 + c[2]z / (1+c[3]z/(1+\dots...c[lim]z)))$.