Expert Mathematica & Maple junkies only!

Factual Questions
1

This concerns the EllipticK (complete elliptic integral of the first kind K(m))
and EllipticE (complete elliptic integral of the second kind). I understand that
Maple and Mathematica are computing numerical approximations, but doesn’t
the difference in this case a bit much?

Mathematica 5.0.1.0, Win2k Pro, AMD Duron Processor:
SetPrecision[EllipticE[0.5], 10] (* SetPrecision used get same number of decimal places as Maple *)
1.350643881
SetPrecision[EllipticK[0.5], 10]
1.854074677

Maple 9.01, Win2k Pro, AMD Duron (different machine):
EllipticE(0.5);
1.467462209
EllipticK(0.5);
1.685750355

2

Check that Mathematica and Maple are using the same definitions. ISTR that Mathematica uses an unusual convention for its elliptic functions: rather than an argument of (1-m[sup]2[/sup]sin[sup]2[/sup]t) it uses (1-m sin[sup]2[/sup]t). Does Mathematica’s EllipticE[0.25] give the same results as Maple’s EllipticE[0.5]?

There may be other differences that I don’t remember, too.

3

Omphaloskeptic, you are right! Thank you so much! Less than 30 minutes for a resolution of a problem that, in my opinion, was so obscure! WOW. The teeming millions never cease to amaze me! :slight_smile:

(For comparison, my usenet posts haven’t even shown up yet!)