Abstract.We consider the incomplete hyperelliptic integralwith a > 0, A2 > 0, n > 2, where X belongs to the connected component of {x|A2X2 + Anzn < a} containing the origin. Continuing previous work on the complete hyperelliptic integral, we express in this paper H (a, X) as a convergent series of hypergeometric type. A brief survey of some applications to algebraic equations and mechanics is then given.
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