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~Q_{-\frac{1}{2}}(z)

~=

~
\sqrt{ \frac{2}{z+1} } ~K\biggl( \sqrt{ \frac{2}{z+1}} \biggr)

      for example …

~Q_{-\frac{1}{2}}(\cosh\eta)

~=

~
2 e^{-\eta/2} K(e^{-\eta})

Abramowitz & Stegun (1995), p. 337, eq. (8.13.3)

Abramowitz & Stegun (1995), p. 337, eq. (8.13.4)

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