User:Tohline/Math/EQ PplusHalf01
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<math>~P_{+ 1 / 2}(z)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi} \biggl[z + \sqrt{ z^2-1} \biggr]^{1 / 2} ~E\biggl( \sqrt{ \frac{2(z^2-1)^{1 / 2}}{z + (z^2-1)^{1 / 2}}} \biggr) </math> |
for example … |
<math>~P_{+1 / 2}(\cosh\eta)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi}~e^{\eta/2}~ E( \sqrt{1-e^{-2\eta}} ) </math> |
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Abramowitz & Stegun (1995), p. 337, eq. (8.13.5) |
Abramowitz & Stegun (1995), p. 337, eq. (8.13.6) |
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