Let . The incomplete elliptic integral of the third kind is then defined as
The complete elliptic integral of the second kind
See also Elliptic Integral of the First Kind, Elliptic Integral of the Second Kind, Elliptic Integral Singular Value
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.