Elliptic Delta Function

$$\delta(r)=\sqrt{r}-2\alpha(r),$$

where $\alpha$ is the Elliptic Alpha Function.

See also Elliptic Alpha Function, Elliptic Integral Singular Value

References

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.

Weisstein, E. W. ``Elliptic Singular Values.'' Mathematica notebook EllipticSingular.m.