The following two equations seem to be numerically equal:
$\frac{{{y^{14}}{2^F}1\left( {1,\frac{{15}}{8},\frac{{23}}{8},{y^8}} \right)}}{{15\;{2^F}1\left( {1,\frac{1}{8},\frac{9}{8},{y^8}} \right)}} - {(1 - x)^{7/4}} = 0$
${{{\sinh }^{ - 4}}\left( {\frac{{0.88137}}{x}} \right) - (1 - {y^8}) = 0}$
At $x = 0,\;y = 1\;{\rm{and}}\;{\rm{at}}\;x = 1,\;y = 0$
The second equation is a well known equation in statistical mechanics with $y$ known as magnetization and $x$ is a scaled temperature $(T/{T_c})$ . The first equation containing Gauss hypergeometric series was derived by solving an ordinary differential equation.
x is positive and ranges from 0 to 1.Is it possible to prove that both eqns are identical?