Quasi-Taylor series in the theory of magnetism

Summation formulas are derived for quasi-Taylor series that arise in the diagram technique for spin operators and correspond to $m$-point correlations of the spins. In the approximation of self-consistent pair correlations, we obtain an equation of state of an Ising ferromagnet $(d=3)$ valid in a wide range of temperatures and magnetic fields except for a narrow neighborhood of the critical point. In the same approximation, we calculate the shape of the magnetic resonance line of the Ising ferromagnet; it is Gaussian. In the limit $T\to\infty$, complete summation of the quasi- Taylor series yields an exact expression for the line shape.