Addendum -- Elliptic Functions on MAPLE
After Chapter 6 was posted I became aware that MAPLE has greatly updated and
improved their support of Elliptic Functions in MAPLE V Releases 4 &
5. This is further indication of the recent increase in interest in
the Elliptic Functions.
Here are some of the changes:
- The former procedure LegendreF is now called
EllipticF. The arguments and syntax are the same.
- EllipticK(k) = EllipticF(1,k) is the complete
elliptic integral, whereas the complementary complete elliptic
integral is EllipticCK.
Further, MAPLE has now implemented the Jacobi elliptic functions. In
particular we now have:
- JacobiAM(t,k) is the Jacobi amplitude function,
that is, our function phi.
- JacobiSN(t,k) is the sn function.
- JacobiCN(t,k) is the cn function.
- JacobiDN(t,k) is the dn function.
In addition there are functions JacobiNS, JacobiNC,
JacobiND which are the reciprocals of sn, cn and dn
respectively. What we call tn= sn/cn MAPLE calls
JacobiSC, likewise there are functions
JacobiCS, JacobiSD, JacobiDS, JacobiCD, JacobiDC which
are cn/sn, sn/dn, dn/sn, cn/dn and dn/cn respectively.
Finally, the help pages are slightly more helpful than the old ones,
but no replacement for our text.