Template:Math/EQ PplusHalf01

	$P_{+\frac{1}{2}}(z)$	$=$	$\frac{2}{\pi }[z+\sqrt{z^2-1}{]}^{1/2}E(\sqrt{\frac{2(z^2-1{)}^{1/2}}{z+(z^2-1{)}^{1/2}}})$	for example …	$P_{+\frac{1}{2}}(\cosh \eta )$	$=$	$\frac{2}{\pi }{e}^{\eta /2}E(\sqrt{1-e^{-2\eta }})$
Abramowitz & Stegun (1995), p. 337, eq. (8.13.5)					Abramowitz & Stegun (1995), p. 337, eq. (8.13.6)