Verify that expression (15) of Section 14.2 indeed satisfies the functional equation (14) for the field-free Ising model in one dimension. Next show (or at least verify) that, with the field present, the functional equation (11), with \(\boldsymbol{K}^{\prime}\) given by (8), is satisfied by the more general expression

\[
f\left(K_{1}, K_{2}\right)=-\ln \left[e^{K_{1}} \cosh K_{2}+\left\{e^{-2 K_{1}}+e^{2 K_{1}} \sinh ^{2} K_{2}\right\}^{1 / 2}\right]
\]