Chapter 11.12, Problem 3P

Computer plot graphs of $K(k)$ and $E(k)$ in (12.3) for $k$ from 0 to $1 .$ Also plot $3\text{D}$ graphs of $F(\varphi ,k)$ and $E(\varphi ,k)$ in (12.1) for $k$ from 0 to 1 and $\varphi$ from 0 to $\pi /2$ and also from 0 to $2\pi .$ Warning: Be sure you understand the notation used by your computer program; see text discussion just after (12.3) and Example 1.