Template:Math/EQ PplusHalf01

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Revision as of 18:07, 29 June 2024 by Joel2 (talk | contribs) (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/SpecialFunctions#Toroidal_Function_Evaluations </td> <td align="right"> <math>P_{+ \frac{1}{2}}(z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <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> </td> <td align="center" rowspa...")

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

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