User:Tohline/Math/EQ PminusHalf01
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<math>~P_{-\frac{1}{2}}(z)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi} \biggl[\frac{2}{z+1}\biggr]^{1 / 2} ~K\biggl( \sqrt{ \frac{z-1}{z+1}} \biggr) </math> |
for example … |
<math>~P_{-\frac{1}{2}}(\cosh\eta)</math> |
<math>~=</math> |
<math>~ \biggl[ \frac{\pi}{2} \cdot \cosh \frac{\eta}{2} \biggr]^{-1} K\biggl( \tanh \frac{\eta}{2} \biggr) </math> |
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Abramowitz & Stegun (1995), p. 337, eq. (8.13.1) |
Abramowitz & Stegun (1995), p. 337, eq. (8.13.2) |
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