Cf. Dunkl et De. Ramirez, ALGORITHM-736 - HYPERELLIPTIC INTEGRALS AND THE SURFACE MEASURE OF ELLIPSOIDS, ACM transactions on mathematical software, 20(4), 1994, pp. 427-435
The algorithm for computing a class of hyperelliptic integrals and for
determining the surface measure of ellipsoids is described in detail
by Dunkl and Ramirez [1994]. An efficient implementation of their algo
rithm is presented here.