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Dunkl, Ramirez. Hyperelliptic integrals, algorithm(T)(14s).djvu |
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Size 0.2Mb Date Dec 18, 2004 |
semiaxes for the ellipsoid in Un, given by
м u' -1- EД)
and let the surface measure of this ellipsoid be denoted by ^?\8г,..., 8n)...
Computing Hyperelliptic Integrals for Ellipsoids • 423
Note that E.10) yields a lower bound for ||| Г ||| with
E.11)
which is weaker than the lower bound given by Theorem 4.1, since the
geometric mean is dominated by the arithmetic mean...
With
semiaxes 2, 2, and 1, Lawden's formula D.2.19) shows that the surface area is
34.688...
To overcome this inherent
problem, we propose the expected radius |||M~1(^)||| as an all-purpose
geometric measure of the size of the ellipsoid e(?)...
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