In 1985, Louis de Branges de Bourcia proved the Bieberbach conjecture, i.e., for a univalent function its [n.sup.th] Taylor coefficient
is bounded by n (see ).
By using the Taylor expansion (5) for f [member of] [SIGMA](p) and the Taylor coefficient
estimate (6) for |[a.su.n]|, we have for 0 < r < p,
Note, however, that even for moderate steady-state inflation, it takes a large coefficient on output to generate determinacy in a rule that includes the standard Taylor coefficient
, [f.sub.y] = 0.125, on output.
On the other hand, it is well known (see e.g., ) that the value [sigma]([z.sub.i]) of the parameter a in (2.8) at the interpolation node [z.sub.i] completely determines the ([n.sub.i] + 1)-th Taylor coefficient
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
As a result, we get a linear system for which the solution of this system yields the unknown Taylor coefficients
of the solution functions.
Clearly, the third equality in (22) is concerned with Markov parameters, which are defined as Taylor coefficients
of the transfer function in the frequency domain when it is expanded around the infinity .
This is so because the coefficients [c.sub.n] are the Taylor coefficients
at u = 0 of the function h(u) = g(t)[dt/du], which is defined in an implicit form because, in general, the function t(u) is not explicitly known.
If f [member of] [S.sup.0.sub.H] for which f(D) is convex, Clunie and Sheil- Small  proved that the Taylor coefficients
of h and g satisfy the inequalities
Then, the Taylor coefficients
of f(z) are given by the following finite sum
Following this procedure, which can be easily programmed using symbolic algebra , the Taylor coefficients
up to a desired order n can be obtained.
Here [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] [member of] C and the [a.sub.j] are the Taylor coefficients
For identical diodes, [g.sub.1] = [g'.sub.1], [g.sub.2] = -[g'.sub.2], [g.sub.3] = [g'.sub.3], [c.sub.1] = [c'.sub.1], [c.sub.2] = -[c'.sub.2] and [c.sub.3] = [c'.sub.3], hence, [Y.sub.1] = [Y'.sub.1] [g.sub.i] and [c.sub.i] for i = 1 to 3 are the first three Taylor coefficients
of the conductances and capacitors of the diode, respectively.