Template:Math/EQ EllipticIntegral03

	$K(\mu )$	$=$	$\ln \frac{4}{k^{\text{'}}}+\frac{1}{2^2}(\ln \frac{4}{k^{\text{'}}}-\frac{2}{1\cdot 2})(k^{\prime }{)}^2+(\frac{1\cdot 3}{2\cdot 4}{)}^2(\ln \frac{4}{k^{\text{'}}}-\frac{2}{1\cdot 2}-\frac{2}{3\cdot 4})(k^{\prime }{)}^4+(\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}{)}^2(\ln \frac{4}{k^{\text{'}}}-\frac{2}{1\cdot 2}-\frac{2}{3\cdot 4}-\frac{2}{5\cdot 6})(k^{\prime }{)}^6+\cdots$
Gradshteyn & Ryzhik (1965), §8.113.3
where:   $k^{\text{'}}\equiv (1-{\mu }^2{)}^{1/2}$