# 6.   Singularity Analysis of Generating Functions

## VI.1

Use the standard function scale to directly derive an asymptotic expression for the number of strings in this following CFG: S = E + U×Z×S + D×Z×S, U = Z + U×U×Z, D = Z + D×D×Z.

## VI.2

Give an asymptotic expression for the number of rooted ordered trees for which every node has 0, 2, or 3 children. How many bits are necessary to represent such a tree?

## Program VI.1

In the style of the plots in Lecture 6, do $r$- and $\theta$-plots of $1/\Gamma(z)$ in the unit square  of size 10 centered at the origin. Click here for access to the Java code used for the lecture.