#!/bin/sh 

# $Id: r-from-kappa.awk,v 1.1 2005/04/21 16:02:14 rajo Exp $

# Author: Lubomir Host 'rajo' <host8 AT kepler.fmph.uniba.sk>
# Description: compute PSV from \kappa


# Run this with awk:
exec awk '

function r1(k)
{ return ( (2 + k*k + sqrt(4 + k*k*k*k)) / (2*k) ); }

function r2(k)
{ return ( (1 + k + k*k + (1 + k)*sqrt(1 + k*k)) / (  k) ); }

function r3(k)
{ return ( (1 + 2*k*k + sqrt(1 + 4*k*k*k*k)) / (2*k) ); }


// {
	printf "(r 1/2)_0     = %g\n", r1($1);
	printf "(r 1/2)_z     = %g\n", r2($1);
	printf "(r 1/2)_{ext} = %g\n", r3($1);
}

' $* # end of awk script