Let . The incomplete elliptic integral of the third kind is then defined as

(1) | |||

(2) |

where is a constant known as the Characteristic.

The complete elliptic integral of the second kind

(3) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.). ``Elliptic Integrals'' and ``Elliptic Integrals of the Third Kind.''
Ch. 17 and §17.7 in *Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables, 9th printing.* New York: Dover, pp. 587-607, 1972.

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1999-05-25